How many triangles are possible given m∠B = 95°, b = 24, a = 5?

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Answer 1 · 2018-02-25T07:09:10

Only one triangle possible.

$a = 5, b = 24, c = 23$

$hatA = 12^@, hat B = 95^@, hat C = 73^@$

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Applying Law of Sines,

$sin A = (a sin B) / b = (5 * sin 95) / 24 = 0.2075$

$hat A = sin ^-1 0.2075 ~~ 12^@$

$hat C = 180 - 95 - 12 = 73^@$

$c = (b sin C) / sin B = (24 sin 73) / sin 95 ~~ 23$