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 \(\rm ∠ C = \dfrac {9π -10}{20}\)
