Question

by first finding cos x, work out the size of angle x. give your answer to 1 d.p. bookwork code: 5e calculator allowed not drawn accurately 28.9 mm 13.4 mm

Explanation:

Step1: Recall cosine - ratio formula

In a right - triangle, $\cos x=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, the adjacent side to angle $x$ is $13.4$ mm and the hypotenuse is $28.9$ mm. So, $\cos x=\frac{13.4}{28.9}$.

Step2: Calculate the value of $\cos x$

$\cos x=\frac{13.4}{28.9}\approx0.4637$.

Step3: Find the value of $x$

$x = \cos^{- 1}(0.4637)$. Using a calculator, $x\approx62.4^{\circ}$ (to 1 decimal place).

Answer:

$62.4^{\circ}$