Question

there is a right triangle vwu with right angle at v. the length of side v w is 7.5, the length of side w u is 9.5, and the angle at u is x degrees. we need to find the value of x. answer: x = input box °. submit answer

Explanation:

Step1: Identify triangle type and trigonometric function

We have a right - triangle \( \triangle VWU \) with right angle at \( V \). We know the length of the opposite side to angle \( x \) (which is \( VW = 7.5 \)) and the length of the hypotenuse \( WU=9.5 \). The sine function is defined as \( \sin(x)=\frac{\text{opposite}}{\text{hypotenuse}} \). So, \( \sin(x)=\frac{7.5}{9.5} \).

Step2: Calculate the value of \( x \)

First, calculate \( \frac{7.5}{9.5}\approx0.7895 \). Then, to find \( x \), we take the inverse sine (arcsin) of \( 0.7895 \). So, \( x = \arcsin(0.7895) \). Using a calculator, we find that \( x\approx52.1^{\circ} \) (rounded to one decimal place).

Answer:

\( x\approx52.1 \)