Question

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

Explanation:

Step1: Identify trigonometric ratio

We know that in right - triangle $UVW$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 28^{\circ}$, the adjacent side to $\angle U$ is $x$ and the opposite side is $4$. So, $\tan(28^{\circ})=\frac{4}{x}$.

Step2: Solve for $x$

Cross - multiply to get $x\times\tan(28^{\circ}) = 4$. Then $x=\frac{4}{\tan(28^{\circ})}$.

Step3: Calculate the value of $x$

We know that $\tan(28^{\circ})\approx0.5317$. So, $x=\frac{4}{0.5317}\approx7.5$.

Answer:

$7.5$