Question

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

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle at T. For angle U (66°), side ST = 7.5 is the opposite side, and side UT = x is the adjacent side. Use tangent:
$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Step2: Substitute known values

$\tan(66^\circ) = \frac{7.5}{x}$

Step3: Rearrange to solve for x

$x = \frac{7.5}{\tan(66^\circ)}$

Step4: Calculate value

$\tan(66^\circ) \approx 2.2460$, so:
$x \approx \frac{7.5}{2.2460} \approx 3.3$

Answer:

$3.3$