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InterviewSolution
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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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Answer» 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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