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 $FG = 7.8$, and the adjacent side is $GH = 6$. Use tangent ratio:
$\tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{7.8}{6}$

Step2: Calculate tangent value

Simplify the fraction:
$\tan(x) = 1.3$

Step3: Solve for $x$

Use inverse tangent function:
$x = \arctan(1.3)$
Calculate and round to nearest tenth:
$x \approx 52.4^\circ$

Answer:

$52.4$