Question

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

Explanation:

Step1: Use the sine function

In a right - triangle, the sine of an angle \(x\) is defined as \(\sin x=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the side opposite to angle \(x\) is \(v = 9.8\) and the hypotenuse is \(w=8.9\) (Wait, no! Wait, in a right - triangle \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For angle \(x\), the opposite side is \(vw = 9.8\) and the hypotenuse is \(uw\). First, find the hypotenuse using the Pythagorean theorem \(uw=\sqrt{8.9^{2}+9.8^{2}}=\sqrt{79.21 + 96.04}=\sqrt{175.25}\approx13.24\). Then \(\sin x=\frac{9.8}{13.24}\)

Step2: Calculate the angle

\(x=\sin^{- 1}(\frac{9.8}{13.24})\). \(\frac{9.8}{13.24}\approx0.74\). Then \(x=\sin^{-1}(0.74)\approx47.8^{\circ}\)

Answer:

\(47.8\)