Question

A triangle has sides A, B, and C. Sides A and B are of lengths `5` and `7`, respectively, and the angle between A and B is `(3pi)/8`. What is the length of side C?

Answer 1

`C=10.04`

Explanation:

Cosine law states that if two sides `A` and `B` and included angle `gamma` is given than third side `C` is

`C=sqrt(A^2+B^2+2ABcosgamma)`

Here `A=5`, `B=7` and included angle is `(3pi)/8`

Hence `C=sqrt(5^2+7^2+2xx5xx7xxcos((3pi)/8)`

= `sqrt(25+49+70xx0.3827`

= `sqrt(74+26.789)=sqrt100.789=10.04`