Question

4)
in a right triangle, one acute angle is 31°, the length of the adjacent side to this angle is 10, find the length of the hypotenuse marked as x

Explanation:

Step1: Identify trigonometric ratio

We use cosine: $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Substitute known values

$\cos(31^\circ)=\frac{10}{x}$

Step3: Solve for $x$

$x=\frac{10}{\cos(31^\circ)}$
Calculate $\cos(31^\circ)\approx0.8572$, so $x\approx\frac{10}{0.8572}$

Answer:

$x\approx11.67$