Question

solve for x. round to the nearest tenth of a degree, if necessary. triangle with right angle at v, sides: wv=7.5, wu=9.5, angle at u is x°

Explanation:

Step1: Use the sine function

In a right - triangle, the sine of an angle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For angle $U$, the opposite side is $WV = 7.5$ and the hypotenuse is $WU=9.5$. So, $\sin x=\frac{7.5}{9.5}$.

Step2: Solve for \(x\)

Take the inverse sine (arcsin) of both sides: $x = \arcsin(\frac{7.5}{9.5})$.
Calculate $\frac{7.5}{9.5}\approx0.7895$.
Then $x=\arcsin(0.7895)$. Using a calculator, $x\approx52.2^{\circ}$.

Answer:

$52.2^{\circ}$