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Paper 2 · June 2009 · Trigonometry

In a triangle ABC, $\hat{BAC}=\left(\dfrac{\pi}{2}+\theta\right)$ radians and $\hat{ACB}=\left(\theta-\dfrac{\pi}{2}\right)$ radians. Find $\hat{ABC}$ in radians.

Model answer

pi-2theta

Also accepted: π-2θ, pi - 2 theta

Explanation

The angles of a triangle sum to

\pi

radians, so

\hat{ABC}=\pi-\left(\dfrac{\pi}{2}+\theta\right)-\left(\theta-\dfrac{\pi}{2}\right)=\pi-2\theta

.

Derived from ZIMSEC Mathematics Paper 2, June 2009, Q3

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