Question

solve for x. round to the nearest tenth of a degree, if necessary.
answer attempt 1 out of 2
x =

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle \( \triangle OPQ\) with right - angle at \(P\), we know the opposite side (\(PQ = 5.7\)) and the hypotenuse (\(OQ=8.7\)). We use the sine ratio. The sine of an angle \(x\) in a right - triangle is given by \(\sin x=\frac{\text{opposite}}{\text{hypotenuse}}\).

So, \(\sin x=\frac{5.7}{8.7}\).

Step2: Solve for \(x\)

We have \(x = \sin^{- 1}(\frac{5.7}{8.7})\).
First, calculate \(\frac{5.7}{8.7}\approx0.6552\).
Then, \(x=\sin^{-1}(0.6552)\).
Using a calculator, \(x\approx40.9^{\circ}\) (rounded to the nearest tenth of a degree).

Answer:

\(40.9\)