Question

find wx.
write your answer as an integer or as a decimal rounded to the nearest tenth.
wx =
submit

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(WXY\), we know the hypotenuse \(WY = 9\) and the angle \(\angle Y=34^{\circ}\), and we want to find the side \(WX\) (opposite to \(\angle Y\)). The sine ratio is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin Y=\frac{WX}{WY}\).

Step2: Substitute the values

Substitute \(Y = 34^{\circ}\) and \(WY = 9\) into the sine formula. We get \(\sin(34^{\circ})=\frac{WX}{9}\).

Step3: Solve for \(WX\)

Multiply both sides of the equation by \(9\): \(WX = 9\times\sin(34^{\circ})\).
Using a calculator, \(\sin(34^{\circ})\approx0.5592\). Then \(WX=9\times0.5592 = 5.0328\approx5.0\)

Answer:

\(5.0\)