Two poles are ‘a’ metres apart and the height of one is double of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the smaller is

$\frac{a}{{\sqrt 2 }}\,{\text{metres}}$$

$\sqrt {2a} \,{\text{metres}}$$

$\frac{a}{{2\sqrt 2 }}\,{\text{metres}}$$

$\frac{a}{{\sqrt 2 }}\,{\text{metres}}$$

The angles of depression of two ships from the top of a light house are 45° and 30° towards east. If the ships are 100 m apart, the height of the light house is

$50\left( {\sqrt 3+ 1} \right)m$$

$50\left( {\sqrt 3- 1} \right)m$$

$50\left( {\sqrt 3+ 1} \right)m$$

From a lighthouse the angles of depression of two ships on opposite sides of the light house are observed to be 30° and 45°. If the height of the lighthouse is h metres, the distance between the ships is

$\left( {\sqrt 3- 1} \right)\,h\,{\text{metres}}$$

$\left( {\sqrt 3+ 1} \right)\,h\,{\text{metres}}$$

$\left( {\sqrt 3- 1} \right)\,h\,{\text{metres}}$$

$\sqrt 3 \,h\,{\text{metres}}$$

${\text{1 + }}\left( {1 + \frac{1}{{\sqrt 3 }}} \right)\,h\,{\text{metres}}$$

A boy is standing at the top of the tower and another boy is at the ground at some distance from the foot of the tower, then the angle of elevation and depression between the boys when both look at a each other will be-

ngle of elevation will be greater

annot be predicted for relation

ngle of depression will be greater

The angles of elevation of the top of from two points P and Q at distance $${{m^2}}$$ and $${{n^2}}$$ respectively, from the base and in the same straight line with it are complementary. The height of the tower is-

${\left( {mn} \right)^{\frac{1}{2}}}$$

The angle of depression of a point situated at a distance of 70m from the base of a tower is 60°. The height of the tower is-

[\frac{{70\sqrt 3 }}{3}{\text{ m}}\]

Two persons are on either sides of a tower of height 50 m. The persons observers the top of the tower at an angle of elevation of 30° and 60°. If a car crosses these two persons in 10 seconds, what is the speed of the car?

$\frac{{20\sqrt 3 }}{3}\,{\text{km/hr}}$$

$\frac{{24}}{{\sqrt 3 }}\,{\text{km/hr}}$$

A vertical pole fixed to the ground is divided in the ratio 1 : 9 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a place on the ground, 15 m away from the base of the pole, what is the height of the pole?

${\text{15}}\sqrt 5 \,{\text{m}}$$

${\text{60}}\sqrt 3 \,{\text{m}}$$

1449 + Mcqs in Height and Distance in General Aptitude Page 29 McqOptions

1401.	From the top of a cliff 25 m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is
A.	5 m
B.	0 m
C.	5 m
D.	00 m
Answer» C. 5 m

Discussion

1402.	Two poles are ‘a’ metres apart and the height of one is double of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the smaller is
A.	$\sqrt {2a} \,{\text{metres}}$$
B.	$\frac{a}{{2\sqrt 2 }}\,{\text{metres}}$$
C.	$\frac{a}{{\sqrt 2 }}\,{\text{metres}}$$
D.	$2a\,{\text{metres}}$$
Answer» C. $\frac{a}{{\sqrt 2 }}\,{\text{metres}}$$

Discussion

1403.	A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall is
A.	$15\sqrt 3 \,m$$
B.	$\frac{{15\sqrt 3 }}{2}\,m$$
C.	$\frac{{15}}{2}\,m$$
D.	$15\,m$$
Answer» C. $\frac{{15}}{2}\,m$$

Discussion

1404.	If the angles of elevation of a tower from two points distance a and b (a > b) from its foot and in the same straight line from it are 30° and 60°, then the height of the tower is?
A.	$\sqrt {a + b} $$
B.	$\sqrt {ab} $$
C.	$\sqrt {a - b} $$
D.	$\sqrt {\frac{a}{b}} $$
Answer» C. $\sqrt {a - b} $$

Discussion

1405.	The angle of depression of a car, standing on the ground, from the top of a 75 m tower, is 30°. The distance of the car from the base of the tower (in metres) is
A.	5 $$\sqrt 3 $$
B.	0 $$\sqrt 3 $$
C.	5 $$\sqrt 3 $$
D.	50
Answer» D. 50

Discussion

1406.	The angles of depression of two ships from the top of a light house are 45° and 30° towards east. If the ships are 100 m apart, the height of the light house is
A.	$\frac{{50}}{{\sqrt 3+ 1}}m$$
B.	$\frac{{50}}{{\sqrt 3- 1}}m$$
C.	$50\left( {\sqrt 3- 1} \right)m$$
D.	$50\left( {\sqrt 3+ 1} \right)m$$
Answer» D. $50\left( {\sqrt 3+ 1} \right)m$$

Discussion

1407.	If the angle of elevation of a tower from a distance of 100 metres from its foot is 60?, the height of the tower is
A.	$100\sqrt 3 \,m$$
B.	$\frac{{100}}{{\sqrt 3 }}\,m$$
C.	$50\sqrt 3 \,m$$
D.	$\frac{{200}}{{\sqrt 3 }}\,m$$
Answer» B. $\frac{{100}}{{\sqrt 3 }}\,m$$

Discussion

1408.	Two persons are 'a' meters apart and the height of one is double that of the other. If from the middle point of the line joining their feet, an observer finds the angular elevation of their tops to be complementary, then the height of the shorter post is
A.	$\frac{a}{4}$$
B.	$\frac{a}{{\sqrt 2 }}$$
C.	$a\sqrt 2 $$
D.	$\frac{a}{{2\sqrt 2 }}$$
Answer» E.

Discussion

1409.	If the height of a vertical pole is $$\sqrt 3 $$ times the length of its shadow on the ground, then the angle of elevation of the sun at that time is
A.	0°
B.	0°
C.	5°
D.	5°
Answer» C. 5°

Discussion

1410.	If a 1.5 m tall girl stands at a distance of 3 m from a lamp-post and casts a shadow of length 4.5 m on the ground, then the height of the lamp-post is
A.	.5 m
B.	m
C.	.5 m
D.	.8 m
Answer» D. .8 m

Discussion

1411.	From a lighthouse the angles of depression of two ships on opposite sides of the light house are observed to be 30° and 45°. If the height of the lighthouse is h metres, the distance between the ships is
A.	$\left( {\sqrt 3+ 1} \right)\,h\,{\text{metres}}$$
B.	$\left( {\sqrt 3- 1} \right)\,h\,{\text{metres}}$$
C.	$\sqrt 3 \,h\,{\text{metres}}$$
D.	${\text{1 + }}\left( {1 + \frac{1}{{\sqrt 3 }}} \right)\,h\,{\text{metres}}$$
Answer» B. $\left( {\sqrt 3- 1} \right)\,h\,{\text{metres}}$$

Discussion

1412.	From the top of a tower, the angles of depression of two objects P and Q (situated on the ground on the same side of the tower) separated at a distance of 100$${\left( {3 - \sqrt 3 } \right)}$$m are 45° and 60 ° respectively. The height of the tower is-
A.	00 m
B.	50 m
C.	00 m
D.	one of these
Answer» D. one of these

Discussion

1413.	TF is a tower with F on the ground. The angle of elevation of T from A is x° such that tan x°= $$\frac{2}{5}$$and AF = 200 m. The angle of elevation of T from a nearer point B is y° with BF = 80 m. The value of y° is-
A.	5°
B.	5°
C.	0°
D.	0°
Answer» C. 0°

Discussion

1414.	The top of a 15 metre high tower makes an angle of elevation of 60° with the bottom of an electric pole and angle of elevation of 30° with the top of the pole. What is the height of electric pole ?
A.	meters
B.	meters
C.	0 meters
D.	2 meters
E.	one of these
Answer» D. 2 meters

Discussion

1415.	A man is watching from the top of tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man’s eye when at a distance of 60 meters from the tower. After 5 seconds, the angle of depression becomes 30°. What is the approximate speed of the boat, assuming that it is running in still water?
A.	2 kmph
B.	6 kmph
C.	8 kmph
D.	0 kmph
E.	2 kmph
Answer» B. 6 kmph

Discussion

1416.	The angle of elevation of a cloud from a point 200 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°. The height of the cloud is-
A.	00 m
B.	00 m
C.	00 m
D.	00 m
Answer» B. 00 m

Discussion

1417.	A boy is standing at the top of the tower and another boy is at the ground at some distance from the foot of the tower, then the angle of elevation and depression between the boys when both look at a each other will be-
A.	qual
B.	ngle of elevation will be greater
C.	annot be predicted for relation
D.	ngle of depression will be greater
Answer» B. ngle of elevation will be greater

Discussion

1418.	The angles of elevation of the top of from two points P and Q at distance $${{m^2}}$$ and $${{n^2}}$$ respectively, from the base and in the same straight line with it are complementary. The height of the tower is-
A.	${\left( {mn} \right)^{\frac{1}{2}}}$$
B.	$m{n^{\frac{1}{2}}}$$
C.	${m^{\frac{1}{2}}}n$$
D.	$mn$$
Answer» E.

Discussion

1419.	If a 30 m ladder is placed against a 15 m wall such that it just reaches the top of the wall, then the elevation of the wall is equal to-
A.	5°
B.	0°
C.	0°
D.	0°
Answer» C. 0°

Discussion

1420.	A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from 30° to 45°, how soon after this will the car reach the observation tower ?
A.	4 min. 35 sec.
B.	5 min. 49 sec.
C.	6 min. 23 sec.
D.	8 min. 5 sec.
Answer» D. 8 min. 5 sec.

Discussion

1421.	The angle of depression of a point situated at a distance of 70m from the base of a tower is 60°. The height of the tower is-
A.	[35\sqrt 3 {\text{ m}}\]
B.	[70\sqrt 3 {\text{ m}}\]
C.	[\frac{{70\sqrt 3 }}{3}{\text{ m}}\]
D.	[{\text{70 m}}\]
Answer» C. [\frac{{70\sqrt 3 }}{3}{\text{ m}}\]

Discussion

1422.	On the same side of tower, two objects are located. Observed from the top of the tower, their angles of depression are 45° and 60°. If the height of the tower is 150 m, the distance between the objects is-
A.	3.5 m
B.	6.9 m
C.	6.7 m
D.	0 m
Answer» B. 6.9 m

Discussion

1423.	The angle of elevation of the top of a tower from a certain point is 30°. If the observed moves 20 m towards the tower, the angle of elevationthe angle of elevation of top of the tower increases by 15°. The height of the tower is
A.	7.3 m
B.	1.9 m
C.	7.3 m
D.	0 m
Answer» D. 0 m

Discussion

1424.	The angle of elevation of the sun, when the length of the shadow of a tree √3 times the height of the tree, is:
A.	0º
B.	5º
C.	0º
D.	0º
Answer» B. 5º

Discussion

1425.	The elevation of the summit of a mountain from its foot is 45°. After ascending 2 km towards the mountain upon an incline of 30°,the elevation changes to 60°. What is the approximate height of the mountain?
A.	.2 km
B.	.6 km
C.	.4 km
D.	.7 km
Answer» E.

Discussion

1426.	From a tower of 80 m high, the angle of depression of a bus is 30°. How far is the bus from the tower?
A.	0 m
B.	38.4 m
C.	6.24 m
D.	60 m
Answer» C. 6.24 m

Discussion

1427.	From the foot and the top of a building of height 230 m, a person observes the top of a tower with angles of elevation of b and a respectively. What is the distance between the top of these buildings if tan a = $$\frac{5}{{12}}$$ and tan b = $$\frac{4}{{5}}$$
A.	00 m
B.	50 m
C.	00 m
D.	50 m
Answer» E.

Discussion

1428.	Two vertical poles are 200 m apart and the height of one is double that of the other. From the middle point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary. Find the heights of the poles.
A.	41 m and 282 m
B.	0.5 m and 141 m
C.	5 m and 130 m
D.	30 m and 260 m
Answer» C. 5 m and 130 m

Discussion

1429.	A man on the top of a vertical observation tower observers a car moving at a uniform speed coming directly towards it. If it takes 8 minutes for the angle of depression to change from 30° to 45°, how soon after this will the car reach the observation tower?
A.	min 17 second
B.	0 min 57 second
C.	4 min 34 second
D.	2 min 23 second
Answer» C. 4 min 34 second

Discussion

1430.	Two persons are on either sides of a tower of height 50 m. The persons observers the top of the tower at an angle of elevation of 30° and 60°. If a car crosses these two persons in 10 seconds, what is the speed of the car?
A.	$24\sqrt 3 \,{\text{km/hr}}$$
B.	$\frac{{20\sqrt 3 }}{3}\,{\text{km/hr}}$$
C.	$\frac{{24}}{{\sqrt 3 }}\,{\text{km/hr}}$$
D.	one of these
Answer» B. $\frac{{20\sqrt 3 }}{3}\,{\text{km/hr}}$$

Discussion

1431.	The angle of elevation of the sun, when the length of the shadow of a tree is equal to the height of the tree, is:
A.	0°
B.	0°
C.	5°
D.	one of these
Answer» D. one of these

Discussion

1432.	An aeroplane when 900 m high passes vertically above another aeroplane at an instant when their angles of elevation at same observing point are 60° and 45° respectively. Approximately, how many meters higher is the one than the other?
A.	81 m
B.	69 m
C.	54 m
D.	11 m
Answer» B. 69 m

Discussion

1433.	A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man's eye when at a distance of 100 metres from the tower. After 10 seconds, the angle of depression becomes 30°. What is the approximate speed of the boat, assuming that it is running in still water?
A.	6.28 km/hr
B.	2.42 km/hr
C.	4.22 km/hr
D.	1.25 km/hr
Answer» B. 2.42 km/hr

Discussion

1434.	A vertical pole fixed to the ground is divided in the ratio 1 : 9 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a place on the ground, 15 m away from the base of the pole, what is the height of the pole?
A.	$60\sqrt 5 \,{\text{m}}$$
B.	${\text{15}}\sqrt 5 \,{\text{m}}$$
C.	$15\sqrt 3 \,{\text{m}}$$
D.	${\text{60}}\sqrt 3 \,{\text{m}}$$
Answer» B. ${\text{15}}\sqrt 5 \,{\text{m}}$$

Discussion

1435.	A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 45º. What is the distance between the base of the tower and the point P?
A.	units
B.	$3\sqrt 3 $$ units
C.	ata inadequate
D.	2 units
Answer» D. 2 units

Discussion

1436.	A ladder 10 m long just reaches the top of a wall and makes an angle of 60° with the wall.Find the distance of the foot of the ladder from the wall $$\left( {\sqrt 3= 1.73} \right)$$
A.	.32 m
B.	7.3 m
C.	m
D.	.65 m
Answer» E.

Discussion

1437.	The angle of elevation of the top of the tower from a point on the ground is $${\sin ^{ - 1}}\left({\frac{3}{5}} \right).$$If the point of observation is 20 meters away from the foot of the tower, what is the height of the tower?
A.	m
B.	8 m
C.	5 m
D.	2 m
Answer» D. 2 m

Discussion

1438.	The angles of depression and elevation of the top of a wall 11 m high from top and bottom of a tree are 60° and 30° respectively. What is the height of the tree?
A.	2 m
B.	4 m
C.	3 m
D.	one of these
Answer» C. 3 m

Discussion

1439.	From a point P on a level ground, the angle of elevation of the top tower is 30º. If the tower is 200 m high, the distance of point P from the foot of the tower is:
A.	46 m
B.	00 m
C.	12 m
D.	98 m
Answer» B. 00 m

Discussion

1440.	When the sun's altitude changes from 30° to 60°, the length of the shadow of a tower decreases by 70m. What is the height of the tower?
A.	5 m
B.	40 m
C.	0.6 m
D.	0.2 m
Answer» D. 0.2 m

Discussion

1441.	To a man standing outside his house, the angles of elevation of the top and bottom of a window are 60° and 45° respectively. If the height of the man is 180 cm and he is 5 m away from the wall, what is the length of the window?
A.	.65 m
B.	m
C.	.5 m
D.	.65 m
Answer» E.

Discussion

1442.	A vertical tower stands on ground and is surmounted by a vertical flagpole of height 18 m. At a point on the ground, the angle of elevation of the bottom and the top of the flagpole are 30° and 60° respectively. What is the height of the tower?
A.	m
B.	0.40 m
C.	5.57 m
D.	2 m
Answer» B. 0.40 m

Discussion

1443.	A person, standing exactly midway between two towers, observes the top of the two towers at angle of elevation of 22.5° and 67.5°. What is the ratio of the height of the taller tower to the height of the shorter tower? (Given that tan 22.5° = $$\sqrt 2- 1$$ )
A.	$1 - 2\sqrt 2 :1$$
B.	$1 + 2\sqrt 2 :1$$
C.	$3 + 2\sqrt 2 :1$$
D.	$3 - 2\sqrt 2 :1$$
Answer» D. $3 - 2\sqrt 2 :1$$

Discussion

1444.	An observer 2 m tall is $$10\sqrt 3 $$m away from a tower. The angle of elevation from his eye to the top of the tower is 30º. The height of the tower is:
A.	4 m
B.	2 m
C.	0 m
D.	one of these
Answer» C. 0 m

Discussion

1445.	A balloon leaves the earth at a point A and rises vertically at uniform speed. At the end of 2 minutes, John finds the angular elevation of the balloon as 60°. If the point at which John is standing is 150 m away from point A, what is the speed of the balloon?
A.	.63 meter/sec
B.	.16 meter/sec
C.	.87 meter/sec
D.	.72 meter/sec
Answer» C. .87 meter/sec

Discussion

1446.	Find the angle of elevation of the sun when the shadow of a pole of 18 m height is $$6\sqrt 3 $$ m long?
A.	0°
B.	0°
C.	5°
D.	one of these
Answer» C. 5°

Discussion

1447.	The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 12.4 m away from the wall. The length of the ladder is:
A.	4.8 m
B.	.2 m
C.	2.4 m
D.	4.8 m
Answer» E.

Discussion

1448.	The angle of elevation of the top of a tower from a certain point is 30°. If the observer moves 40 m towards the tower, the angle of elevation of the top of the tower increases by 15°. The height of the tower is:
A.	4.2 m
B.	2.2 m
C.	2.2 m
D.	4.6 m
Answer» E.

Discussion

1449.	Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 200 m high, the distance between the two ships is:
A.	00 m
B.	73 m
C.	46 m
D.	46 m
Answer» D. 46 m

Discussion

Explore topic-wise MCQs in General Aptitude.

From the top of a cliff 25 m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is

Two poles are ‘a’ metres apart and the height of one is double of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the smaller is

A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall is

If the angles of elevation of a tower from two points distance a and b (a > b) from its foot and in the same straight line from it are 30° and 60°, then the height of the tower is?

The angle of depression of a car, standing on the ground, from the top of a 75 m tower, is 30°. The distance of the car from the base of the tower (in metres) is

The angles of depression of two ships from the top of a light house are 45° and 30° towards east. If the ships are 100 m apart, the height of the light house is

If the angle of elevation of a tower from a distance of 100 metres from its foot is 60?, the height of the tower is

Two persons are 'a' meters apart and the height of one is double that of the other. If from the middle point of the line joining their feet, an observer finds the angular elevation of their tops to be complementary, then the height of the shorter post is

If the height of a vertical pole is $$\sqrt 3 $$ times the length of its shadow on the ground, then the angle of elevation of the sun at that time is

If a 1.5 m tall girl stands at a distance of 3 m from a lamp-post and casts a shadow of length 4.5 m on the ground, then the height of the lamp-post is

From a lighthouse the angles of depression of two ships on opposite sides of the light house are observed to be 30° and 45°. If the height of the lighthouse is h metres, the distance between the ships is

From the top of a tower, the angles of depression of two objects P and Q (situated on the ground on the same side of the tower) separated at a distance of 100$${\left( {3 - \sqrt 3 } \right)}$$m are 45° and 60 ° respectively. The height of the tower is-

TF is a tower with F on the ground. The angle of elevation of T from A is x° such that tan x°= $$\frac{2}{5}$$and AF = 200 m. The angle of elevation of T from a nearer point B is y° with BF = 80 m. The value of y° is-

The top of a 15 metre high tower makes an angle of elevation of 60° with the bottom of an electric pole and angle of elevation of 30° with the top of the pole. What is the height of electric pole ?

The angle of elevation of a cloud from a point 200 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°. The height of the cloud is-

A boy is standing at the top of the tower and another boy is at the ground at some distance from the foot of the tower, then the angle of elevation and depression between the boys when both look at a each other will be-

The angles of elevation of the top of from two points P and Q at distance $${{m^2}}$$ and $${{n^2}}$$ respectively, from the base and in the same straight line with it are complementary. The height of the tower is-

If a 30 m ladder is placed against a 15 m wall such that it just reaches the top of the wall, then the elevation of the wall is equal to-

A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from 30° to 45°, how soon after this will the car reach the observation tower ?

The angle of depression of a point situated at a distance of 70m from the base of a tower is 60°. The height of the tower is-

On the same side of tower, two objects are located. Observed from the top of the tower, their angles of depression are 45° and 60°. If the height of the tower is 150 m, the distance between the objects is-

The angle of elevation of the top of a tower from a certain point is 30°. If the observed moves 20 m towards the tower, the angle of elevationthe angle of elevation of top of the tower increases by 15°. The height of the tower is

The angle of elevation of the sun, when the length of the shadow of a tree √3 times the height of the tree, is:

The elevation of the summit of a mountain from its foot is 45°. After ascending 2 km towards the mountain upon an incline of 30°,the elevation changes to 60°. What is the approximate height of the mountain?

From a tower of 80 m high, the angle of depression of a bus is 30°. How far is the bus from the tower?

From the foot and the top of a building of height 230 m, a person observes the top of a tower with angles of elevation of b and a respectively. What is the distance between the top of these buildings if tan a = $$\frac{5}{{12}}$$ and tan b = $$\frac{4}{{5}}$$

Two vertical poles are 200 m apart and the height of one is double that of the other. From the middle point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary. Find the heights of the poles.

A man on the top of a vertical observation tower observers a car moving at a uniform speed coming directly towards it. If it takes 8 minutes for the angle of depression to change from 30° to 45°, how soon after this will the car reach the observation tower?

Two persons are on either sides of a tower of height 50 m. The persons observers the top of the tower at an angle of elevation of 30° and 60°. If a car crosses these two persons in 10 seconds, what is the speed of the car?

The angle of elevation of the sun, when the length of the shadow of a tree is equal to the height of the tree, is:

An aeroplane when 900 m high passes vertically above another aeroplane at an instant when their angles of elevation at same observing point are 60° and 45° respectively. Approximately, how many meters higher is the one than the other?

A vertical pole fixed to the ground is divided in the ratio 1 : 9 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a place on the ground, 15 m away from the base of the pole, what is the height of the pole?

A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 45º. What is the distance between the base of the tower and the point P?

A ladder 10 m long just reaches the top of a wall and makes an angle of 60° with the wall.Find the distance of the foot of the ladder from the wall $$\left( {\sqrt 3= 1.73} \right)$$

The angle of elevation of the top of the tower from a point on the ground is $${\sin ^{ - 1}}\left({\frac{3}{5}} \right).$$If the point of observation is 20 meters away from the foot of the tower, what is the height of the tower?

The angles of depression and elevation of the top of a wall 11 m high from top and bottom of a tree are 60° and 30° respectively. What is the height of the tree?

From a point P on a level ground, the angle of elevation of the top tower is 30º. If the tower is 200 m high, the distance of point P from the foot of the tower is:

When the sun's altitude changes from 30° to 60°, the length of the shadow of a tower decreases by 70m. What is the height of the tower?

To a man standing outside his house, the angles of elevation of the top and bottom of a window are 60° and 45° respectively. If the height of the man is 180 cm and he is 5 m away from the wall, what is the length of the window?

A vertical tower stands on ground and is surmounted by a vertical flagpole of height 18 m. At a point on the ground, the angle of elevation of the bottom and the top of the flagpole are 30° and 60° respectively. What is the height of the tower?

A person, standing exactly midway between two towers, observes the top of the two towers at angle of elevation of 22.5° and 67.5°. What is the ratio of the height of the taller tower to the height of the shorter tower? (Given that tan 22.5° = $$\sqrt 2- 1$$ )

An observer 2 m tall is $$10\sqrt 3 $$m away from a tower. The angle of elevation from his eye to the top of the tower is 30º. The height of the tower is:

A balloon leaves the earth at a point A and rises vertically at uniform speed. At the end of 2 minutes, John finds the angular elevation of the balloon as 60°. If the point at which John is standing is 150 m away from point A, what is the speed of the balloon?

Find the angle of elevation of the sun when the shadow of a pole of 18 m height is $$6\sqrt 3 $$ m long?

The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 12.4 m away from the wall. The length of the ladder is:

The angle of elevation of the top of a tower from a certain point is 30°. If the observer moves 40 m towards the tower, the angle of elevation of the top of the tower increases by 15°. The height of the tower is:

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 200 m high, the distance between the two ships is: