Question

In MNO, n = 88 inches, m = 60 inches and M=38°. Find all possible values of N,to the nearest 10th of a degree.

Answer 1

Given:

In triangle MNO,

$\begin{gathered} n=88inches \\ m=60inches \\ \angle M=38\degree \end{gathered}$

Required:

To find the angle N.

Explanation:

According to the sine rule

$\frac{\sin M}{m}=\frac{\sin N}{n}$

Now

$\begin{gathered} \frac{\sin38}{60}=\frac{\sin N}{88} \\ \\ \frac{0.6156}{60}\times88=\sin N \\ \\ \sin N=0.9028 \\ \\ \angle N=\sin^{-1}(0.9028) \\ \\ \angle N=64.55\degree \end{gathered}$

Or

$\begin{gathered} \angle N=180-64.55 \\ =115.45\degree \end{gathered}$

Final Answer:

The possible values of N are,

$\angle N=64.5\degree,115.5\degree$