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 $34$, adjacent side is $48$. Use tangent: $\tan(x) = \frac{\text{opposite}}{\text{adjacent}}$
<Expression>$\tan(x) = \frac{34}{48}$</Expression>

Step2: Simplify the fraction

Reduce the fraction to simplest form.
<Expression>$\tan(x) = \frac{17}{24} \approx 0.7083$</Expression>

Step3: Solve for $x$

Use inverse tangent function to find $x$.
<Expression>$x = \tan^{-1}(0.7083)$</Expression>

Step4: Calculate and round

Compute the value and round to nearest tenth.
<Expression>$x \approx 35.3^\circ$</Expression>

Answer:

$35.3^\circ$