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Malik Dev Dial
Asked: 2022-11-08T00:04:01+05:30 In:

One of the angles of a triangle is 1/2 radian and the other is 99°. What is the third angle in radian measure? 
1. \(\dfrac{9\pi – 10}{\pi}\)
2. \(\dfrac{90\pi – 100}{7\pi}\)
3. \(\dfrac{90\pi – 10}{\pi}\)
4. None of the above

One of the angles of a triangle is 1/2 radian and the other is 99°. What is the third angle in radian measure? 
1. \(\dfrac{9\pi – 10}{\pi}\)
2. \(\dfrac{90\pi – 100}{7\pi}\)
3. \(\dfrac{90\pi – 10}{\pi}\)
4. None of the above
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  1. Correct Answer – Option 4 : None of the above

    Concept:

    The sum of all angles of a triangle is 180° = π 

    Calculations:

    Given, one of the angles of a triangle is 1/2 radian and the other is 99°.

    ⇒ \(\rm ∠ A = (\dfrac 1 2)^c\) and ∠B = 99° 

    Convert the ∠B  into radians by multiplying by \(\rm \dfrac {π}{180^\circ}\).

    ⇒ \(∠ B = 99^\circ \times \dfrac {π}{180^\circ}\) = \(\dfrac {11π}{20}\)

    As we know, the sum of all angles of a triangle is 180° = π

    ⇒ \(\rm ∠ A + ∠ B + ∠ C = π\)

    ⇒ \(\rm ∠ C = π – (∠ A + ∠ B)\)

    ⇒ \(\rm ∠ C = π – (\dfrac 12 + \dfrac{11π}{20})\)

    ⇒  \(\rm ∠ C = π – (\dfrac {10 + 11π}{20})\)

    ⇒  \(\rm ∠ C = \dfrac {9π -10}{20}\)

    Hence, one of the angles of a triangle is 1/2 radian and the other is 99°, then the third angle in radian measure is \(\rm ∠ C = \dfrac {9π -10}{20}\)

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