Question

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

Explanation:

Step1: Identify the trigonometric ratio

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 \(QR = 5.7\) and the hypotenuse is \(PR=7\).

Step2: Calculate the angle \(x\)

We have \(\sin x=\frac{5.7}{7}\). Then \(x = \sin^{- 1}(\frac{5.7}{7})\).

$$x=\sin^{-1}(0.8143)$$

Using a calculator, \(x\approx54.5^{\circ}\)

Answer:

\(x\approx54.5^{\circ}\)