What is the measure of angle N?

 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 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.

Okay so for every triangle has three angles that always add up to 180 degrees. and to tell the difference between whether they are secure, right or obtuse is that acute: has one angle that is less than 90 degrees. right triangle means there is at least one angle that is exactly 90 degrees. and an obtuse angle has an angle that is bigger than 180 degrees. i’ll do #13 as an example: 13. 40 and 50 so if every triangle has 180 degrees 40+50= 90 degrees then180-90= 90 degrees so the third angle is 90 degrees and because this triangle has a 90 degree angle it means it is a right triangle