Question

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

Explanation:

Step1: Identify trigonometric relation

We use the cosine function since $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 72^{\circ}$, the adjacent side to the $72^{\circ}$ angle 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 $\cos(72^{\circ})\approx0.3090$. Then $x = 94\times0.3090=28.946$.

Step3: Round the result

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

Answer:

$28.9$