Question

a) write the value of sin θ for the right - angled triangle below as a fraction. b) using your answer to part a), work out the size of angle θ. give your answer to 1 d.p.

Explanation:

Step1: Recall sine - definition

In a right - angled triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. The opposite side to angle $\theta$ is $13$ cm and the hypotenuse is $18$ cm.
So, $\sin\theta=\frac{13}{18}$.

Step2: Find the angle $\theta$

We know that $\theta = \sin^{- 1}(\sin\theta)$. Since $\sin\theta=\frac{13}{18}$, then $\theta=\sin^{-1}(\frac{13}{18})$.
Using a calculator, $\theta=\sin^{-1}(\frac{13}{18})\approx46.4^{\circ}$ (to 1 d.p.)

Answer:

a) $\sin\theta=\frac{13}{18}$
b) $46.4^{\circ}$