Question

8)
in a right triangle, one acute angle is 24°, the adjacent side to this angle is 20, 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

$\cos(24^\circ)=\frac{20}{x}$

Step3: Rearrange to solve for x

$x=\frac{20}{\cos(24^\circ)}$

Step4: Calculate the value

$\cos(24^\circ)\approx0.9135$, so $x\approx\frac{20}{0.9135}\approx21.9$

Answer:

$x\approx21.9$