Question

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

Explanation:

Step1: Identify adjacent side, hypotenuse

Adjacent to $\angle Q$: $PQ=8$, hypotenuse: $OQ=x$, $\angle Q=75^\circ$

Step2: Use cosine definition

$\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$
$\cos(75^\circ)=\frac{8}{x}$

Step3: Rearrange to solve for x

$x=\frac{8}{\cos(75^\circ)}$

Step4: Calculate value

$\cos(75^\circ)\approx0.2588$, so $x\approx\frac{8}{0.2588}\approx30.9$

Answer:

$30.9$