Question

multiple choice 1 point
in $\triangle lmn$, $m\angle l = 108^{\circ}$, $m\angle m = 25^{\circ}$ and $\ell = 12$. what is $m$?
27
about 0.19
about 5.3
about 20.8

Explanation:

Step1: Apply the Law of Sines

The Law of Sines states that \(\frac{\ell}{\sin L}=\frac{m}{\sin M}\).

Step2: Substitute the given values

We know that \(\ell = 12\), \(L = 108^{\circ}\), \(M=25^{\circ}\). So, \(\frac{12}{\sin108^{\circ}}=\frac{m}{\sin25^{\circ}}\).

Step3: Solve for \(m\)

First, find \(\sin108^{\circ}\approx0.9511\) and \(\sin25^{\circ}\approx0.4226\). Then \(m=\frac{12\times\sin25^{\circ}}{\sin108^{\circ}}\). Substitute the values: \(m=\frac{12\times0.4226}{0.9511}\approx5.3\).

Answer:

about \(5.3\)