solve for (x). round to the nearest tenth, if necessary.\nanswer attempt 1 out of 2\n(x =)

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle PON, we know the adjacent side to the given angle $\angle N = 32^{\circ}$ is $ON = 73$ and we want to find the hypotenuse $PN=x$. We use the cosine function since $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. So, $\cos(32^{\circ})=\frac{73}{x}$.

Step2: Solve for $x$

Cross - multiply to get $x\cos(32^{\circ}) = 73$. Then $x=\frac{73}{\cos(32^{\circ})}$. We know that $\cos(32^{\circ})\approx0.848$. So, $x=\frac{73}{0.848}\approx86.1$.

Answer:

$86.1$