Question

1 fill in the blank 1 point
find the angle measure(s). round to the nearest tenth if needed.
in \\( \triangle w x y, m \angle x=104^{\circ}, x=7 \\), and \\( y=2 \\). find \\( m \angle y \\).
the \\( m \angle y= \\) type your answer...
2 fill in the blank 1 point
a path in a park forms a triangle as shown. what is the measure of angle a? round to the nearest tenth of a degree.
\\( m \angle a \approx \\) type your answer...
3 fill in the blank 1 point
what is the length of y?
round to the nearest tenth. \\( y \approx \\) type your answer...

Explanation:

Step1: Apply the Law of Sines

The Law of Sines states that in a triangle \(\triangle WXY\), \(\frac{\sin X}{x}=\frac{\sin Y}{y}\). We know that \(m\angle X = 104^{\circ}\), \(x = 7\), and \(y = 2\). Substituting these values into the Law of Sines formula gives \(\frac{\sin104^{\circ}}{7}=\frac{\sin Y}{2}\).

Step2: Solve for \(\sin Y\)

Cross - multiply the equation \(\frac{\sin104^{\circ}}{7}=\frac{\sin Y}{2}\) to get \(2\sin104^{\circ}=7\sin Y\). Then \(\sin Y=\frac{2\sin104^{\circ}}{7}\). Since \(\sin104^{\circ}\approx0.97\), we have \(\sin Y=\frac{2\times0.97}{7}=\frac{1.94}{7}\approx0.277\).

Step3: Find \(m\angle Y\)

Take the inverse sine of \(0.277\), so \(m\angle Y=\sin^{- 1}(0.277)\approx16.1^{\circ}\)

Answer:

\(16.1\)