Question

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

Explanation:

Step1: Identify adjacent side/hypotenuse

For $\angle P=60^\circ$, adjacent side is $x$, hypotenuse $PN=9$.

Step2: Use cosine ratio

$\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$
$\cos(60^\circ)=\frac{x}{9}$

Step3: Solve for $x$

$x=9\times\cos(60^\circ)$
$x=9\times0.5=4.5$

Answer:

$4.5$