Question

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?

Answer 1

`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