9514 1404 393
Answer:
21.8 cm
Step-by-step explanation:
A useful way to write the Law of Sines relation when solving for side lengths is ...
a/sin(A) = b/sin(B)
Then the solution for 'a' is found by multiplying by sin(A):
a = sin(A)(b/sin(B)) = b·sin(A)/sin(B)
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We need to know the angle A. Its value is ...
A = 180° -75° -31.8° = 73.2°
Then the desired length is ...
a = (22 cm)sin(73.2°)/sin(75°) ≈ (22 cm)(0.9573/0.9659)
a ≈ 21.8 cm
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I like to use the longest side and largest angle in the equation when those are available. That is why I chose 75° and 22 cm.
