Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the cosine of an angle is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 63^{\circ}$, the adjacent side $a = 13$, and the hypotenuse is $x$. So, $\cos63^{\circ}=\frac{13}{x}$.

Step2: Solve for \(x\)

Rearrange the formula $\cos63^{\circ}=\frac{13}{x}$ to get $x=\frac{13}{\cos63^{\circ}}$.
We know that $\cos63^{\circ}\approx0.454$.
Then $x=\frac{13}{0.454}\approx28.6$.

Answer:

$28.6$