Use the sine rule to find two triangles where: ∠A = 49∘, a = 29, b = 32.?

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1 Answer
May 2, 2018

Case 1 : #color(purple)( hat B = 56.39^@, hat C = 74.61^@#

Case 2 : #color(crimson)( hat B = 123.61^@, hat C = 7.39^@#

Explanation:

As per Law of Sines,

#a / sin A = b / sin B = c / sin C#

#hat A = 49^@, a = 29, b = 32#

#sin B = (b * sin A) / a = (32 * sin 49) / 29 = 0.8328#

#hat B = sin ^-1 (0.8328) = 56.39^@#

Since # sin B = sin (180 - B) = sin (180 - 56.39) = sin 123.61^@#

Case 1. #hat C = 180 - hat A - hat B = 180 - 49 - 56.39 = 74.61^@#

Case 2 #hat C = 180 - hat A - hat B = 180 - 49 - 123.61 = 7.39^@#