Question

What is the measure of angle N?

Answer 1

Answer:

∠N = 61°

Step-by-step explanation:

We can use the fact that $\frac{a}{sin(A)}=\frac{b}{sin(B)}=\frac{c}{sin(C)}$ to solve for the missing angle.

In this case, we have $\frac{m}{sin(M)}=\frac{n}{sin(N)}=\frac{o}{sin(O)}$

So we need to solve for ∠N, so we should manipulate one of the equations that involves the variable N. I will choose to use the equations with N and O since we have the measure of side o

Since  $\frac{n}{sin(N)}=\frac{o}{sin(O)}$, solving for N would give us $\frac{nsin(O)}{o} = sin(N)$ and then getting N by itself would give us $N=sin^{-1} (\frac{nsin(O)}{o})$

Plugging in the respective values would give us  $N=sin^{-1} (\frac{18sin(17)}{6}) =sin^{-1} (3sin(17))=sin^{-1} (0.877)= 61.3^{o}$

∠N = 61°