Question

1 multiple choice 1 point
in \\( \triangle l m n, m \angle l=108^{\circ}, m \angle m=25^{\circ} \\) and \\( \ell=12 \\). what is \\( m \\)?
27
about 0.19
about 5.3
about 20.8
2 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...
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 \(\frac{\sin L}{l}=\frac{\sin M}{m}\).
Given \(m\angle L = 108^{\circ}\), \(l = 12\), and \(m\angle M=25^{\circ}\).
Substitute the values into the formula: \(\frac{\sin(108^{\circ})}{12}=\frac{\sin(25^{\circ})}{m}\).

Step2: Solve for \(m\)

First, find \(\sin(108^{\circ})\approx0.9511\) and \(\sin(25^{\circ})\approx0.4226\).
The equation becomes \(\frac{0.9511}{12}=\frac{0.4226}{m}\).
Cross - multiply: \(0.9511m = 12\times0.4226\).
\(0.9511m=5.0712\).
Then \(m=\frac{5.0712}{0.9511}\approx5.3\).

Answer:

C. about 5.3