Question

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 \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, for angle \(x\), the side opposite to \(x\) is \(IJ = 23\) and the hypotenuse is \(IK=53\). So, \(\sin x=\frac{23}{53}\).

Step2: Solve for \(x\)

Take the inverse - sine (arcsin) of both sides. \(x=\sin^{- 1}(\frac{23}{53})\). Using a calculator, \(\frac{23}{53}\approx0.434\). Then \(x=\sin^{-1}(0.434)\).

Answer:

\(x\approx25.7^{\circ}\)