How do you solve the triangle given A=52, a=190, b=200?

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How do you solve the triangle given A=52, a=190, b=200?

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Answer 1 · 2018-02-18T13:29:14

$a = 190, b = 200, c = 229.2641$ $color(brown)(a = 190, b = 200, c = 229.2641$

$ˆ A = 52^{\circ}, ˆ B = {56.0372}^{\circ}, ˆ C = 71.9628$ $color(green)(hatA = 52^@, hatB = 56.0372^@, hatC = 71.9628$

Explanation:

$ˆ A = 52^{\circ}, a = 190, b = 200$ $hat A = 52^@, a = 190, b = 200$

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

#sin B = (b sin B) / a = (200 sin 52) / 190 = 0.8294

$ˆ B = {sin}^{- 1} 0.8294 = {56.0372}^{\circ}$ $hatB = sin ^(-1) 0.8294 =color(green)( 56.0372^@$

$ˆ C = 180 - 52 - 56.0372 = 71.9628$ $hatC = 180 - 52 - 56.0372 = color (green)(71.9628$

$c = \frac{a sin C}{sin A} = \frac{190 \cdot sin (71.9628)}{sin 52} = 229.2641$ $c = (a sin C ) / sin A = (190 * sin (71.9628))/sin 52= color(brown)(229.2641)$ #

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How do you solve the triangle given A=52, a=190, b=200?

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