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.

Step-by-step explanation:

According to the sine rule

`(\sin M)/(m)=(\sin N)/(n)`

Now

`\begin{gathered} (\sin38)/(60)=(\sin N)/(88) \\ \\ (0.6156)/(60)*88=\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`