Answer:
61°
Step-by-step explanation:
Given:
∆MNO,
Side MO (n) = 18
MN (o) = 6
m<O = 17°
Required:
m<N
Solution:
Using the sine rule, [tex] \frac{sin N}{n} = \frac{sin O}{o} [/tex] , solve for N.
Plug in the values of M, n, and m
[tex] \frac{sin N}{18} = \frac{sin 17}{6} [/tex]
Cross multiply
[tex] 6*sin(N) = sin(17)*18 [/tex]
[tex] 6*sin(N) = 0.292*18 [/tex]
Divide both sides by 6
[tex] \frac{6*sin N}{6} = \frac{0.292*18}{6} [/tex]
[tex] sin N = \frac{0.292*18}{6} [/tex]
[tex] sin N = \frac{5.256}{6} [/tex]
[tex] sin N = 0.876 [/tex]
[tex] N = sin^-1(0.876) [/tex]
[tex] N = 61.16 [/tex]
m<N ≈ 61°
