Question

A triangle has sides A, B, and C. The angle between sides A and B is `(pi)/2`. If side C has a length of `8` and the angle between sides B and C is `pi/12`, what is the length of side A?

Answer 1

`A=2(sqrt6-sqrt2)`

Explanation:

Since the given triangle is a right triangle (`hat(AB)=pi/2`),

let's appy the following rule:

`A=C*sin hat(BC)`

`=8*sin(pi/12)`

`=cancel8^2*(sqrt6-sqrt2)/cancel4`

`=2(sqrt6-sqrt2)`