Question

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

Explanation:

Step1: Identify the trigonometric ratio

We know that in a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 72^{\circ}$, the adjacent side to the angle $\theta$ is $x$ and the hypotenuse is 94.
So, $\cos(72^{\circ})=\frac{x}{94}$.

Step2: Solve for $x$

Multiply both sides of the equation by 94: $x = 94\times\cos(72^{\circ})$.
We know that $\cos(72^{\circ})\approx0.309$.
So, $x = 94\times0.309$.
$x=94\times0.309 = 28.946$.

Step3: Round to the nearest tenth

Rounding 28.946 to the nearest tenth gives $x\approx28.9$.

Answer:

$28.9$