Question

find ( mangle y ).
write your answer as an integer or as a decimal rounded to the nearest tenth.
( mangle y=) 。

Explanation:

Step1: Use the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\angle Y\), the opposite side to \(\angle Y\) is \(WX\) (length \(3\)) and the hypotenuse is \(YX\) (length \(4\)). So, \(\sin Y=\frac{3}{4}\).

Step2: Find the angle

To find \(m\angle Y\), we use the inverse sine function. \(m\angle Y = \sin^{-1}(\frac{3}{4})\). Using a calculator, \(\sin^{-1}(0.75)\approx48.6^{\circ}\).

Answer:

\(48.6\)