Question

right triangle quiz a

1. solve for $x$. round to the nearest tenth, if necessary

Explanation:

Step1: Identify trigonometric ratio

In right - triangle $PQR$, we know the adjacent side to angle $P$ ($PQ = 24$) and we want to find the hypotenuse ($PR=x$). We use the cosine function since $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 62^{\circ}$, adjacent side $a = 24$, and hypotenuse $c=x$. So, $\cos(62^{\circ})=\frac{24}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{24}{\cos(62^{\circ})}$. We know that $\cos(62^{\circ})\approx0.4695$. Then $x=\frac{24}{0.4695}\approx51.1$.

Answer:

$51.1$