A triangle has sides A, B, and C. Sides A and B are of lengths #3# and #14#, respectively, and the angle between A and B is #pi/6#. What is the length of side C?

1 Answer
Jan 14, 2016

Answer:

c ≅11.5

Explanation:

Law of cosines: #c^2 = a^2 + b^2 - 2ab cos Theta#
Where a and b are sides opposite angles A and B and #Theta# is the included angle.

In this example #a=3, b=14 and Theta = pi/6#

Therefore: #c^2 = 3^2 + 14^2 - 2. 3.14 cos(pi/6)#
#c^2~= 9 + 196 - 84 * 0.8660254038 #
#c ~= sqrt(132.25386608)#
#c ~= +- 11.5# But c must be +ve

Therefore #c ~= 11.5#