Question

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

Explanation:

Step1: Identify trigonometric ratio

For angle $x^\circ$, the opposite side is $FG=57$, adjacent side is $EF=63$. Use tangent: $\tan(x) = \frac{\text{opposite}}{\text{adjacent}}$
$\tan(x) = \frac{57}{63}$

Step2: Simplify the fraction

Reduce the fraction to simplify calculation.
$\tan(x) = \frac{19}{21} \approx 0.9048$

Step3: Solve for x using arctangent

Apply inverse tangent to find $x$.
$x = \arctan(0.9048)$

Step4: Calculate and round value

Use a calculator to compute, then round to nearest tenth.
$x \approx 42.2^\circ$

Answer:

$42.2^\circ$