Question

What is the measure of angle N?

Answer 1

Answer:  A) 61 degrees

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Work Shown:

Apply the law of sines

sin(N)/MO = sin(O)/MN

sin(N)/18 = sin(17)/6

sin(N) = 18*sin(17)/6

sin(N) = 0.87711511416821 ................. which is approximate

N = arcsin(0.87711511416821)

N = 61.296295678111

N = 61 degrees approximately

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Notes:

• Arcsine is the same as inverse sine. Your calculator is likely to have a button labeled $\sin^{-1}$ to indicate inverse sine.
• There are two solutions to sin(N) = 0.877; however, the other solution for N is larger than 90. This triangle your teacher is showing appears to be an acute triangle where every angle is less than 90 degrees. Technically two triangles are possible with these current given sides and angle.