Question

right angle trigonometry
for the right triangle below, find the length of x.
question help: video

Explanation:

Step1: Identify trigonometric ratio

We know the adjacent - side to the given angle and we want to find the hypotenuse. We use the cosine ratio $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 38^{\circ}$ and the adjacent side $a = 10$, and the hypotenuse is $x$. So, $\cos38^{\circ}=\frac{10}{x}$.

Step2: Solve for $x$

Cross - multiply to get $x\cos38^{\circ}=10$. Then $x=\frac{10}{\cos38^{\circ}}$. Since $\cos38^{\circ}\approx0.788$, $x=\frac{10}{0.788}\approx12.7$.

Answer:

$x\approx12.7$