Question

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

Explanation:

Step1: Use sine function

In a right - triangle, the sine of an angle is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For angle \(J\), the opposite side to angle \(J\) is \(HI = 9\) and the hypotenuse is \(HJ=18\). So \(\sin x=\frac{HI}{HJ}\).
Substitute \(HI = 9\) and \(HJ = 18\) into the formula: \(\sin x=\frac{9}{18}\).

Step2: Simplify the fraction

Simplify \(\frac{9}{18}=\frac{1}{2}\). So \(\sin x=\frac{1}{2}\).

Step3: Find the angle \(x\)

We know that if \(\sin x = k\), then \(x=\sin^{- 1}(k)\). Since \(\sin x=\frac{1}{2}\), then \(x=\sin^{-1}(\frac{1}{2})\).
Using the inverse - sine function, \(x = 30^{\circ}\) (because \(\sin30^{\circ}=\frac{1}{2}\)).

Answer:

\(30^{\circ}\)