Answer:
424.3 in
Explanation:
You want the measure of side l in ∆LMN with m = 450 in, M = 74°, and N = 41°.
Law of sines
The triangle can be solved using the law of sines:
l/sin(L) = m/sin(M)
Angle L is the third angle in the triangle:
L = 180° -74° -41° = 65°
Then the side length is ...
l = m·sin(L)/sin(M) = (450 in)·sin(65°)/sin(74°) ≈ 424.3 in
The length of l is about 424.3 inches.
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