Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle $OPN$ with right - angle at $O$, we know the adjacent side to the given angle $\angle P = 41^{\circ}$ is $x$ and the hypotenuse is $83$. We use the cosine function since $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. So, $\cos(41^{\circ})=\frac{x}{83}$.

Step2: Solve for $x$

Multiply both sides of the equation $\cos(41^{\circ})=\frac{x}{83}$ by $83$ to get $x = 83\times\cos(41^{\circ})$.
We know that $\cos(41^{\circ})\approx0.7547$. Then $x = 83\times0.7547$.
$x=83\times0.7547 = 62.6401$.

Step3: Round the result

Rounding $62.6401$ to the nearest tenth gives $x\approx62.6$.

Answer:

$62.6$