How do you solve the triangle given a = 9, b = 8, and α = 75 degrees?

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How do you solve the triangle given a = 9, b = 8, and α = 75 degrees?

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Answer 1 · 2015-12-03T10:41:06

As you haven't specified which angle is between which sides, let me assume that $alpha$ is the angle that is opposite to $a$ , $beta$ is the angle opposite to $b$ and $gamma$ is the angle opposite to $c$ .

With this assumption, you can use the law of sines to solve your problem:

$sin alpha / a = sin beta / b = sin gamma / c$

1) First, with $a$ , $b$ and $alpha$ given, you can find $beta$ :

$sin beta = sin alpha / a * b = sin 75^@ / 9 * 8$

$=> beta = arcsin ( sin 75^@ / 9 * 8) ~~ 59.16^@$

2) As next, you can determine $gamma$ since $alpha + beta + gamma = 180^@$ must hold in any triangle:

$gamma = 180^@ - alpha - beta = 180^@ - 75^@ - beta ~~ 45.84^@$

3) Finally, you can use the law of sines again to compute $c$ :

$c = a / sin alpha * sin gamma ~~ 6.588$

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How do you solve the triangle given a = 9, b = 8, and α = 75 degrees?

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