Question

Given a = 690 m, b = 673 m, and c = 415 m, find the measures of the angles A, B, and C to the nearest hundredth.

Answer 1

The first step is use the Law of Cosines
see
http://www.khanacademy.org/math/trigonometry/less-basic-trigonometry/trig_iden_tutorial/v/law-of-cosines

for some background.

Answer 2

First find the angle alpha which would be the angle opposite of the longest side, in this case side a.
\[a ^{2}=b ^{2}+c ^{2}-2bc \cos \alpha\]

Answer 3

law of cosines:)

cosC = a^2+b^2-c^2/2ab

cosB=a^2+c^2-b^2/2ac

cosA=b^2+c^2-a^2/2bc

Answer 4

Your second step will be to find the smallest angle which will be gamma opposite the shortest side c. You should use law of sin with that.

Answer 5

and your last step will be the easiest, beta=180-(alpha+gamma)