SOLUTION: A triangle has side lengths 12 ft, 13 ft, and 14 ft. Find the measure of the angle opposite the side of length 13 ft. Round your answer to the nearest tenth of a degree.

Algebra ->  Trigonometry-basics -> SOLUTION: A triangle has side lengths 12 ft, 13 ft, and 14 ft. Find the measure of the angle opposite the side of length 13 ft. Round your answer to the nearest tenth of a degree.      Log On


   

Question 453942: A triangle has side lengths 12 ft, 13 ft, and 14 ft. Find the measure of the angle opposite the side of length 13 ft. Round your answer to the nearest tenth of a degree.
Answer by J2R2R(94) About Me  (Show Source):
You can put this solution on YOUR website!
Using the cosine rule we have:

a^2 = b^2 + c^2 - 2bc Cos A

Rearrange to have
(b^2 + c^2 - a^2)/2bc = Cos A


So if A is the angle opposite the side of length 13ft, we have a=13 and we can have b=12 and c=14. It doesn’t matter if b=14 and c=12 we get the same result a long as a=13).

(144 + 196 - 169)/336 = 171/336 = Cos A

A = 59.4 degrees