Question

solve for x in the triangle. round your answer to the nearest tenth.

Explanation:

Step1: Identify trigonometric ratio

We know that $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 64^{\circ}$, the adjacent - side to the angle $\theta$ is 8, and the hypotenuse is $x$. So, $\cos64^{\circ}=\frac{8}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{8}{\cos64^{\circ}}$. Since $\cos64^{\circ}\approx0.4384$, then $x = \frac{8}{0.4384}\approx18.2$.

Answer:

$18.2$