solve for $x$. round to the nearest tenth of a degree, if necessary.\n\nanswer\nattempt 1 out of 2\n$x =…

solve for $x$. round to the nearest tenth of a degree, if necessary.\n\nanswer\nattempt 1 out of 2\n$x = \\square^{\\circ}$ submit answer

solve for $x$. round to the nearest tenth of a degree, if necessary.\n\nanswer\nattempt 1 out of 2\n$x = \\square^{\\circ}$ submit answer

Answer

Explanation:

Step1: Identify the trigonometric ratio

In the right triangle $VWU$, the side opposite to angle $x$ is $VW = 7.5$ and the hypotenuse is $WU = 9.5$. $$\sin(x) = \frac{\text{opposite}}{\text{hypotenuse}}$$

Step2: Substitute the known values

Substitute the given lengths into the sine ratio formula. $$\sin(x) = \frac{7.5}{9.5}$$

Step3: Solve for $x$ using inverse sine

Apply the inverse sine function to find the measure of the angle. $$x = \arcsin\left(\frac{7.5}{9.5}\right)$$

Step4: Calculate the numerical value

Compute the value and round to the nearest tenth. $$x \approx 52.1301...^{\circ}$$

Answer:

$x = 52.1^{\circ}$