Question

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

Explanation:

Step1: Identify trigonometric ratio

Since we have a right - triangle with opposite side ($7.4$) and adjacent side ($12$) to angle $x$, we use the tangent function. $\tan(x)=\frac{\text{opposite}}{\text{adjacent}}$. So, $\tan(x)=\frac{7.4}{12}$.

Step2: Solve for $x$

We take the inverse tangent of both sides. $x = \tan^{- 1}(\frac{7.4}{12})$.
Using a calculator, $\frac{7.4}{12}\approx0.6167$. Then $x=\tan^{-1}(0.6167)$.
$x\approx31.7^{\circ}$ (rounded to the nearest tenth of a degree).

Answer:

$x\approx31.7^{\circ}$