How many triangles are possible given m∠C = 63°, b = 9, c = 12?

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Answer 1 · 2018-03-26T03:36:57

$color(green)("Only one triangle possible with following measurements."$

$color(blue)(hat A = 75.06^@, hat B = 41.94^@, hat C = 63^@$

$color(red)(a = 13.01, b = 9, c = 12$

$"Given : " b = 9, c = 12, hat C = 63^@$

Applying Law of Sines,

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

$sin B = (b * sin C) / c = (9 * sin 63) / 12 = 0.6683$

$hat B = sin _1 (0.6683) = 41.94^@$

$hat A = 180 - 41.94 - 63 = 75.06@$

a = (c * sin A) / sin C = (12 * sin 75.06) / sin 63 = 13.01#

$color(green)("Only one triangle possible with following measurements."$

$color(blue)(hat A = 75.06^@, hat B = 41.94^@, hat C = 63^@$

$color(red)(a = 13.01, b = 9, c = 12$