Answers:
- Problem 13) M, N, L
- Problem 14) N, L, M
For each answer above, the angles are sorted from smallest to largest.
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Explanation:
The general rule used here is: the smallest side is always opposite the smallest angle. Similarly, the largest side is always opposite the largest angle. This trick only works for triangles.
For problem 13, the smallest angle is M because the shortest side is opposite this angle (side NL = 12). The largest side is MN = 21, making the angle opposite this (angle L) to be the largest angle.
We do not need to compute the actual angle values, though you could if you wanted. To find the angle values, you would use the law of cosines. The steps for this are fairly lengthy, so I'll just use the trick mentioned above.
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Problem 14 is the same idea. Here LM = 7 is the shortest side this time, leading to angle N as the opposite angle that's the smallest of the three angles. Angle M is the largest angle because NL = 14 is the longest side.
