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 is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For angle \(x\), the side opposite to \(x\) is \(HI = 9\), and the hypotenuse \(HJ=18\). So, \(\sin x=\frac{HI}{HJ}\).

Step2: Substitute the values

Substitute \(HI = 9\) and \(HJ = 18\) into the sine formula: \(\sin x=\frac{9}{18}\).
Simplify \(\frac{9}{18}=\frac{1}{2}\). So, \(\sin x=\frac{1}{2}\).

Step3: Find the angle \(x\)

We know that if \(\sin x = a\), then \(x=\sin^{- 1}(a)\). 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:

\(30^{\circ}\)