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MCQOPTIONS
This section includes 91 Mcqs, each offering curated multiple-choice questions to sharpen your Heights & Distances knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
An aeroplane when flying at a height of 4000m from the ground passes vertically above another aeroplane at an instant when the angles of the elevation of the two planes from the same point on the group |
| A. | 1490.53 m |
| B. | 1590.53 m |
| C. | 1690.53 m |
| D. | 1790.53 m |
| Answer» D. 1790.53 m | |
| 2. |
At the foot of a mountain the elevation of its summit is 45 ; after ascending 1000 m towards the mountain up a slope of 30 inclination is found to be 60 . Find the height of the mountain. |
| A. | 1.366 km |
| B. | 1.477 m |
| C. | 1.788 km |
| D. | 1.922 km |
| Answer» B. 1.477 m | |
| 3. |
There is a small island in middle of 100 m wide river and a tall tree stands on island. P and Q are points directly opposite to each other on two banks. If angles of elevation is 30 and 45 . |
| A. | 17.7 m |
| B. | 28.8 m |
| C. | 36.6 m |
| D. | 42.2 m |
| Answer» D. 42.2 m | |
| 4. |
From a point on the ground 40 m away from the foot of a tower, the angle of elevation of the top of the tower is 30 . The angle of elevation of the top of a water tank (on the top of the tower) is 45 |
| A. | 22.5, 17.4 m |
| B. | 23.1, 16.9 m |
| C. | 24.1, 15.7 m |
| D. | 25.1, 14.2 m |
| Answer» C. 24.1, 15.7 m | |
| 5. |
A tower is 100 3 metres high. Find the angle of elevation of its top from a point 100 metres away from its foot. |
| A. | 50 |
| B. | 40 |
| C. | 80 |
| D. | 60 |
| Answer» E. | |
| 6. |
A man on cliff observes fishing trawler at angle of depression of 30 which is approaching the shore to point. 6 minutes later, the angle of depression of the trawler is found to be 60 . |
| A. | 1 min |
| B. | 2 min |
| C. | 3 min |
| D. | None of these |
| Answer» D. None of these | |
| 7. |
A boat is being rowed away from a cliff 150m high. At the top of the cliff the angle of depression of the boat changes from 60 to 45 in 2 minutes. Find the speed of the boat. |
| A. | 1.9 km/hr |
| B. | 2.3 km/hr |
| C. | 3.8 km/hr |
| D. | 4.5 km/hr |
| Answer» B. 2.3 km/hr | |
| 8. |
The banks of a river are parallel. A swimmer starts from a point on one of the banks and swims in a straight line inclined to the bank at 45 and reaches the opposite bank at a point 20 m |
| A. | 12.12 m |
| B. | 14.14 m |
| C. | 16.16 m |
| D. | 18.18 m |
| Answer» C. 16.16 m | |
| 9. |
If the angle of elevation of cloud from a point 200 m above a lake is 30 and the angle of depression of its reflection in the lake is 60 , then find the height of the cloud above the lake. |
| A. | 400 m |
| B. | 600 m |
| C. | 800 m |
| D. | 1000 m |
| Answer» B. 600 m | |
| 10. |
The heights of two poles are 80 m and 62.5 m. If the line joining their tops makes an angle of 45 with the horizontal, then find the distance between the poles. |
| A. | 3.5 m |
| B. | 8.5 m |
| C. | 12.5 m |
| D. | 17.5 m |
| Answer» E. | |
| 11. |
Two poles standing on the same side of a tower in a straight line with it, measure the angles of elevation of the top of the tower at 25 and 50 respectively. If the height of the tower is 70 m, find |
| A. | 31.27 m |
| B. | 89.27 m |
| C. | 29.27 m |
| D. | 92.27 m |
| Answer» C. 29.27 m | |
| 12. |
The shadow of a vertical tower on a level ground increases by 10 m when the altitude of the sun changes from 45 to 30 . Find the height of the tower, correct to two decimal places. |
| A. | 12.44 m |
| B. | 13.66 m |
| C. | 14.77 m |
| D. | 15.22 m |
| Answer» C. 14.77 m | |
| 13. |
From a window A, 10 m above ground the angle of elevation of the top C to a tower is x , where tan x = 5/2 and the angle of depression of the foot D of the tower is y , where tan y = 1/4 . Calculate |
| A. | 30 m |
| B. | 70 m |
| C. | 110 m |
| D. | 130 m |
| Answer» D. 130 m | |
| 14. |
The elevation of T, from A is x where tan x = 2/5 and AF = 200 m. The elevation of T from B, where AB = 80 m is y . Calculate : (a)the height of the tower TF, (b)the angle y correct to nearest degree |
| A. | 100 m, 31 |
| B. | 80 m, 34 |
| C. | 60 m, 36 |
| D. | 40 m, 39 |
| Answer» C. 60 m, 36 | |
| 15. |
From the top of a hill, the angle of depression of two consecutive kilometer stones, due east are found to be 30 and 45 respectively. Find the distance of the two stones from the foot of the hill. |
| A. | 1.366 km, 2.366 km |
| B. | 2.366 km, 3.366 km |
| C. | .366 km, 4.366 km |
| D. | None of these |
| Answer» B. 2.366 km, 3.366 km | |
| 16. |
A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60 . When he moves 50 m away from the bank, he finds the angle of elevation to be 30 . |
| A. | 38.3, 19 m |
| B. | 45.3, 32 m |
| C. | 41.3, 28 m |
| D. | 43.3, 25 m |
| Answer» E. | |
| 17. |
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. | 0.6 km |
| B. | 2.7 km |
| C. | 1.2 km |
| D. | 1.4 km |
| Answer» C. 1.2 km | |
| 18. |
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. | 3.65 m |
| B. | 2.5 m |
| C. | 8.65 m |
| D. | 2 m |
| Answer» B. 2.5 m | |
| 19. |
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. | 65 m and 130 m |
| B. | 130 m and 260 m |
| C. | 141 m and 282 m |
| D. | 70.5 m and 141 m |
| Answer» E. | |
| 20. |
On the same side of a 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 600 m, the distance between the objects is approximately equal to : |
| A. | 272 m |
| B. | 254 m |
| C. | 288 m |
| D. | 284 m |
| Answer» C. 288 m | |
| 21. |
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. | 62.2 m |
| B. | 64.2 m |
| C. | 52.2 m |
| D. | 54.6 m |
| Answer» E. | |
| 22. |
When the sun is 30 above the horizontal, Find the length of shadow cast by a building 50m high. |
| A. | 50 3 m |
| B. | 70 3 m |
| C. | 90 3 m |
| D. | 110 3 m |
| Answer» B. 70 3 m | |
| 23. |
If the elevation of the sun changed from 30 to 60 , then find the difference between the lengths of shadows of a pole 15 m high, made at these two positions. |
| A. | 4 3 m |
| B. | 7 3 m |
| C. | 10 3 m |
| D. | 13 3 m |
| Answer» D. 13 3 m | |
| 24. |
The altitude of the sun at any instant is 60 . Find the height of the vertical pole that will cast a shadow of 30 m. |
| A. | 10 3 m |
| B. | 20 3 m |
| C. | 30 3 m |
| D. | 40 3 m |
| Answer» D. 40 3 m | |
| 25. |
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. Find the height of the tower. |
| A. | 20 m |
| B. | 50 m |
| C. | 130 m |
| D. | 170 m |
| Answer» C. 130 m | |
| 26. |
The pilot of a helicopter, at an altitude of 1200m finds that the two ships are sailing towards it in the same direction. The angle of depression of the ships as observed from the helicopter are 60 a |
| A. | 3 m |
| B. | 200 3 m |
| C. | 400 3 m |
| D. | 700 3 m |
| Answer» D. 700 3 m | |
| 27. |
A balloon is connected to a meteorological station by a cable of length 200 m, inclined at 60 to the horizontal. Find the height of the balloon from the ground. Assume that there is no slack in the c |
| A. | 152.9 m |
| B. | 164.6 m |
| C. | 173.2 m |
| D. | 188.4 m |
| Answer» D. 188.4 m | |
| 28. |
A ladder against a vertical wall makes an angle of 45 with the ground. The foot of the ladder is 3m from the wall. Find the length of the ladder. |
| A. | 2.23 m |
| B. | 4.23 m |
| C. | 6.23 m |
| D. | 8.23 m |
| Answer» C. 6.23 m | |
| 29. |
If a vertical pole 6 m high has a shadow of length 2 3 metres, find the angle of elevation of the sun. |
| A. | 10 |
| B. | 20 |
| C. | 40 |
| D. | 60 |
| Answer» E. | |
| 30. |
A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 7m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is 30 and that of the top o |
| A. | 9.562 m |
| B. | 19.562 m |
| C. | 29.562 m |
| D. | 39.562 m |
| Answer» B. 19.562 m | |
| 31. |
From the top of a building 30 m high, the top and bottom of a tower are observed to have angles of depression 30 and 45 respectively. Find the height of the tower. |
| A. | 60(1-1/ 3) m |
| B. | 50(1-1/ 3) m |
| C. | 40(1-1/ 3) m |
| D. | 30(1-1/ 3) m |
| Answer» E. | |
| 32. |
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 mou |
| A. | 12.7 km |
| B. | 22.7 km |
| C. | 2.7 km |
| D. | 32.7 km |
| Answer» D. 32.7 km | |
| 33. |
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 - |
| A. | 44.6 m |
| B. | 54.6 m |
| C. | 64.6 m |
| D. | 74.6 m |
| Answer» C. 64.6 m | |
| 34. |
The top of a 15 metre high tower makes an angle of elevation of 60 with the bottom of an electronic pole and angle of elevation of 30 with the top of the pole. What is the height of the electric pol |
| A. | 10 meters |
| B. | 15 meters |
| C. | 20 meters |
| D. | 25 meters |
| Answer» B. 15 meters | |
| 35. |
A man watching from top of a tower boat speeding away from tower. The boat makes angle of depression of 45 with the man's eye when distance of 100 mtr from tower. After 10 sec, the angle of depressio |
| A. | 23.28 km/hr |
| B. | 24.28 km/hr |
| C. | 25.28 km/hr |
| D. | 26.28 km/hr |
| Answer» B. 24.28 km/hr | |
| 36. |
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 |
| A. | 6 min 57 second |
| B. | 8 min 57 second |
| C. | 10 min 57 second |
| D. | 12 min 57 second |
| Answer» D. 12 min 57 second | |
| 37. |
The shadow of a building is 20 m long when the angle of elevation of the sun is 60 . Find the height of the building. |
| A. | 34.64 m |
| B. | 38.64 m |
| C. | 42.64 m |
| D. | 49.64 m |
| Answer» B. 38.64 m | |
| 38. |
From the top of a temple near a river the angles of depression of both the banks of river are 45 & 30 . If the height of the temple is 100 m then find out the width of the river. |
| A. | 50( 3-1)m |
| B. | 100( 3-1)m |
| C. | 200( 3-1)m |
| D. | 300( 3-1)m |
| Answer» C. 200( 3-1)m | |
| 39. |
The angle of elevation of the top of a tower from a point is 30 . On walking 40 m towards the tower the angle changes to 45 .Find the height of the tower? |
| A. | 40 ( 3+1)m |
| B. | 30 ( 3+1)m |
| C. | 20 ( 3+1)m |
| D. | 10 ( 3+1)m |
| Answer» D. 10 ( 3+1)m | |
| 40. |
The angle of elevation of the top of a tower from a point on the ground is 30 . On walking 100m towards the tower the angle of elevation changes to 60 . Find the height of the tower. |
| A. | 80 3 |
| B. | 70 3 |
| C. | 60 3 |
| D. | 50 3 |
| Answer» E. | |
| 41. |
A tree bent by the wind .The top of the tree meets the ground at an angle of 60 .If the distance between the top of the foot be 8 m then what was the height of the tree? |
| A. | 8( 3-2) |
| B. | 8( 3+2) |
| C. | 8( 3-4) |
| D. | 8( 3+4) |
| Answer» C. 8( 3-4) | |
| 42. |
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 i |
| A. | 1.65 m |
| B. | 2.65 m |
| C. | 3.65 m |
| D. | 4.65 m |
| Answer» D. 4.65 m | |
| 43. |
The thread of a kite is 120 m long and it is making 30 angular elevation with the ground .What is the height of the kite? |
| A. | 60 m |
| B. | 20 m |
| C. | 40 m |
| D. | 10 m |
| Answer» B. 20 m | |
| 44. |
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 |
| A. | 90.5 m and 121 m |
| B. | 80.5 m and 131m |
| C. | 70.5 m and 141 m |
| D. | 60.5 m and 151 m |
| Answer» D. 60.5 m and 151 m | |
| 45. |
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 i |
| A. | 1.13 meter/sec |
| B. | 2.16 meter/sec |
| C. | 3.22 meter/sec |
| D. | 4.48 meter/sec |
| Answer» C. 3.22 meter/sec | |
| 46. |
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. | 11 m |
| B. | 22 m |
| C. | 33 m |
| D. | 44 m |
| Answer» E. | |
| 47. |
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 ( 3 = 1.73 ) |
| A. | 8.65 m |
| B. | 10.65 m |
| C. | 12.65 m |
| D. | 14.65 m |
| Answer» B. 10.65 m | |
| 48. |
On the same side of a 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 600 m, the distance between the object |
| A. | 254 m |
| B. | 264 m |
| C. | 274 m |
| D. | 284 m |
| Answer» B. 264 m | |
| 49. |
Find the angle of elevation of the sun when the shadow of a pole of 18 m height is 6 3 m long? |
| A. | 60 |
| B. | 70 |
| C. | 80 |
| D. | None of these |
| Answer» B. 70 | |
| 50. |
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 ? (Given that tan 22.5 = 2 1 ) |
| A. | 7+2 2: 1 |
| B. | 1+2 2: 1 |
| C. | 5+2 2: 1 |
| D. | |
| Answer» E. | |