Question

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

Explanation:

Step1: Identify trigonometric ratio

In right - triangle $UST$, 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 use the inverse - sine function $x = \sin^{-1}(0.7143)$. Using a calculator, $x=\sin^{-1}(0.7143)\approx45.6^{\circ}$.

Answer:

$45.6^{\circ}$