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

1 Answer
Dec 3, 2015

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#