Question

What is the measure of angle N?

Answer 1

∠N = 61°

Explanation:

We can use the fact that
`(a)/(sin(A))=(b)/(sin(B))=(c)/(sin(C))` to solve for the missing angle.

In this case, we have
`(m)/(sin(M))=(n)/(sin(N))=(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
`(n)/(sin(N))=(o)/(sin(O))`, solving for N would give us
`(nsin(O))/(o) = sin(N)` and then getting N by itself would give us
`N=sin^(-1) ((nsin(O))/(o))`

Plugging in the respective values would give us
`N=sin^(-1) ((18sin(17))/(6)) =sin^(-1) (3sin(17))=sin^(-1) (0.877)= 61.3^(o)`

∠N = 61°