solve for ( x ). round to the nearest tenth, if necessary.\n\nanswer attempt 1 out of 2\n( x = ) \nsubmit…

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle at $T$. For angle $\angle U = 39^\circ$, side $x$ is opposite, and side $TU = 75$ is adjacent. Use tangent: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Step2: Substitute known values

$\tan(39^\circ) = \frac{x}{75}$

Step3: Solve for $x$

Rearrange to isolate $x$: $x = 75 \times \tan(39^\circ)$ Calculate $\tan(39^\circ) \approx 0.8098$, so: $x \approx 75 \times 0.8098 = 60.735$

Step4: Round to nearest tenth

$x \approx 60.7$

Answer:

$x = 60.7$