Question

A triangle has sides A, B, and C. The angle between sides A and B is `(pi)/6`. If side C has a length of `24` and the angle between sides B and C is `( 5 pi)/12`, what are the lengths of sides A and B?

Answer 1

`A` and `B~~46.364`

Explanation:

The third angle (which is between `A` and `C`) is

`pi/6+(5pi)/12+theta=pi`
`theta=(5pi)/12`

Since the angle between `A` and `C` is the same as the angle between `B` and `C` then the triangle is isosceles and length of side `A` is equal to the length of side `B`

We can use the law of sines (the sine of any angle divided by its opposite side is equal to the sine of any other angle divided by its opposite side) to find the lengths `A` and `B`

`(sin(pi/6))/24=(sin((5pi)/12))/A`

`A=(24(sin((5pi)/12)))/(sin(pi/6))~~46.364`

`A=B`

`A` and `B=46.364`