Question

A triangle has sides A, B, and C. The angle between sides A and B is `(pi)/3`. If side C has a length of `1` and the angle between sides B and C is `( 3 pi)/8`, what are the lengths of sides A and B?

Answer 1

`A = C sina/sinc`
`A =sqrt(6+3sqrt(2))/3`

And B Can be calculated as

`B = C sinb/sinc= sin(7/24pi)/(sqrt(3)/2)`

Explanation:

Use sin law:
`A/sina = C/sinc = B/sinb`
`A = C sina/sinc` now we know `c=pi/3; C=1; a=3/8pi; b=7/24pi`
so `A = 1/2 sqrt(2+sqrt(2))/(sqrt(3)/2)`
`A = sqrt(6+3sqrt(2))/3`
And B
Can be calculated as
`B = C sinb/sinc= sin(7/24pi)/(sqrt(3)/2)`