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 the ratio of the length of the opposite side to the length of the hypotenuse. For angle \(x\), the opposite side is \(HI = 9\) and the hypotenuse is \(HJ=18\). So, \(\sin x=\frac{HI}{HJ}\).

Step2: Substitute the values

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

Step3: Find the angle

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

Answer:

\(30\)