Question

fill in the blank 1 point
find the angle measure(s). round to the nearest tenth if needed.
in ( \triangle wxy ), ( mangle x = 104^{circ} ), ( x = 7 ), and ( y = 2 ). find ( mangle y ).
the ( mangle y=) type your answer...( ^{circ} )

Explanation:

Step1: Apply the Law of Sines

The Law of Sines states that \(\frac{\sin X}{x}=\frac{\sin Y}{y}\).
Given \(m\angle X = 104^{\circ}\), \(x = 7\), and \(y = 2\), we substitute these values into the formula: \(\frac{\sin104^{\circ}}{7}=\frac{\sin Y}{2}\).

Step2: Solve for \(\sin Y\)

Cross - multiply to get \(2\sin104^{\circ}=7\sin Y\).
Then \(\sin Y=\frac{2\sin104^{\circ}}{7}\).
Since \(\sin104^{\circ}\approx0.97\), we have \(\sin Y=\frac{2\times0.97}{7}=\frac{1.94}{7}\approx0.28\).

Step3: Find \(m\angle Y\)

Take the inverse sine of \(0.28\), so \(m\angle Y=\sin^{-1}(0.28)\approx16.3^{\circ}\).

Answer:

\(16.3\)