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

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Answer 1 · 2018-03-26T03:36:57

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

$ˆ A = {75.06}^{\circ}, ˆ B = {41.94}^{\circ}, ˆ C = 63^{\circ}$ $color(blue)(hat A = 75.06^@, hat B = 41.94^@, hat C = 63^@$

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

$Given : b = 9, c = 12, ˆ C = 63^{\circ}$ $"Given : " b = 9, c = 12, hat C = 63^@$

Applying Law of Sines,

$\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$ $a / sin A = b / sin B = c / sin C$

$sin B = \frac{b \cdot sin C}{c} = \frac{9 \cdot sin 63}{12} = 0.6683$ $sin B = (b * sin C) / c = (9 * sin 63) / 12 = 0.6683$

$ˆ B = {sin}_{1} (0.6683) = {41.94}^{\circ}$ $hat B = sin _1 (0.6683) = 41.94^@$

$ˆ A = 180 - 41.94 - 63 = 75.06 \circ$ $hat A = 180 - 41.94 - 63 = 75.06@$

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

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

$ˆ A = {75.06}^{\circ}, ˆ B = {41.94}^{\circ}, ˆ C = 63^{\circ}$ $color(blue)(hat A = 75.06^@, hat B = 41.94^@, hat C = 63^@$

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