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How do you solve the triangle given A=80, a=9, b=9.1?

1 Answer

Aug 10, 2018

$ˆ B = {8.7148}^{\circ}, ˆ C = {15.2842}^{\circ}, c = 2.4091$ $color(purple)(hat B = 8.7148^@, hat C = 15.2842^@, c = 2.4091$

Explanation:

$ˆ A = 80^{\circ}, a = 9, b = 9.1$ $hat A = 80^@, a = 9, b = 9.1$

$sin B = \frac{b sin A}{a} = \frac{9.1 \cdot sin 80}{9} = 0.9958$ $sin B = (b sin A) / a = (9.1 * sin 80) / 9 = 0.9958$

$ˆ B = {sin}^{- 1} 0.9958 \approx {84.7158}^{\circ}$ $hat B = sin ^-1 0.9958 ~~ 84.7158^@$

$ˆ C = 180 - 80 - 84.7158 \approx {15.2842}^{\circ}$ $hat C = 180 - 80 - 84.7158 ~~ 15.2842^@$

$c = \frac{a sin C}{sin A} = \frac{9 \cdot sin 15.2842}{sin 80} \approx 2.4091$ $c = (a sin C) / sin A = (9 * sin 15.2842) / sin 80 ~~ 2.4091$

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