Question

solve for $x$. round to the nearest tenth, if necessary.
right triangle $pon$: $angle o = 90^\circ$, $angle p = 60^\circ$, side $pn = 9$, side $po = x$

Explanation:

Step1: Identify trigonometric ratio

We use cosine: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$, where $\theta=60^\circ$, adjacent side is $x$, hypotenuse is 9.

Step2: Substitute values into formula

$\cos(60^\circ) = \frac{x}{9}$

Step3: Solve for $x$

$x = 9 \times \cos(60^\circ)$
Since $\cos(60^\circ)=0.5$, $x = 9 \times 0.5 = 4.5$

Answer:

$4.5$