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. not drawn accurately 17 cm 14 cm

Explanation:

Step1: Recall sine - definition

In a right - angled triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. The side opposite to angle $\theta$ has length $14$ cm and the hypotenuse has length $17$ cm.
So, $\sin\theta=\frac{14}{17}$.

Step2: Find the angle $\theta$

We know that $\theta=\sin^{- 1}(\frac{14}{17})$. Using a calculator, $\theta=\sin^{-1}(\frac{14}{17})\approx54.3^{\circ}$ (to 1 decimal place).

Answer:

a) $\sin\theta=\frac{14}{17}$
b) $\theta\approx54.3^{\circ}$