Question

A triangle has sides A, B, and C. Sides A and B are of lengths `1` and `5`, respectively, and the angle between A and B is `(5pi)/8`. What is the length of side C?

Answer 1

`C = 5.46139 ...`

Explanation:

By the cosine rule we have:

`C^2 = A^2 + B^2 - 2ABcos(hat(BCA))`
`:. C^2 = 1 + 25 - 2(1)(5)cos((5pi)/8)`
`:. C^2 = 26 - 10cos((5pi)/8)`
`:. C^2 = 26 - 10(-0.38268 ...)`
`:. C^2 = 26 + 3.8268 ...`
`:. C = 5.46139 ...`