A triangle has sides A, B, and C. Sides A and B are of lengths #5# and #4#, respectively, and the angle between A and B is #(7pi)/12 #. What is the length of side C?

1 Answer
Dec 31, 2015

Answer:

#c ~= 7.166#

Explanation:

By the Law of Cosines: #c^2 = a^2 + b^2 - 2ab cos(Theta)#
In this example # a=5, b=4, Theta = (7 pi)/12#

Hence #c^2 = 5^2 + 4^2 - 2. 5. 4 cos((7 pi)/12)#
#c^2 = 25 + 16 - 40 cos((7 pi)/12)#

Using a calculator #cos((7 pi)/12) ~= -0.2588190451#

Therefore #c^2 ~= 41 + 40 * 0.2588190451#

#c^2 ~= 51.3527616#
#c ~= +-sqrt(51.3527616)#

Since c must be positive
#c = 7.166# To 3 decimal places