Question

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?

Answer 1

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`