Question

find ( mangle x ).
write your answer as an integer or as a decimal rounded to the nearest tenth.
( mangle x=square^{circ} )

Explanation:

Step1: Recall the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\angle X\), the side opposite \(\angle X\) is \(WY = 5\), and the hypotenuse is \(WX=9\). So, \(\sin X=\frac{WY}{WX}\).

Step2: Calculate \(\sin X\)

Substitute \(WY = 5\) and \(WX = 9\) into the formula: \(\sin X=\frac{5}{9}\approx0.5556\).

Step3: Find \(X\) using the inverse sine function

Since \(X=\sin^{- 1}(\sin X)\), then \(X=\sin^{-1}(0.5556)\). Using a calculator, \(X\approx33.8^{\circ}\).

Answer:

\(33.8\)