Question

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

Explanation:

Step1: Identify trigonometric ratio

In right - triangle UTS, we know the opposite side (UT = 6.5) and the hypotenuse (US = 9.1) with respect to angle \(x\). We use the sine ratio \(\sin x=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin x=\frac{6.5}{9.1}\).

Step2: Calculate the value of \(\sin x\)

\(\sin x=\frac{6.5}{9.1}\approx0.7143\).

Step3: Find the value of \(x\)

We take the inverse - sine of 0.7143, \(x = \sin^{-1}(0.7143)\). Using a calculator, \(x\approx45.6^{\circ}\).

Answer:

\(x\approx45.6^{\circ}\)