Question

We have triangle with `AB=6,hat(A)=pi/3 and hat(B)=pi/4`.How to find `AC and BC`?

Answer 1

See below.

Explanation:

Using the so called sinus law.

`(sin hat C)/[AB] = (sin hat A)/[BC] = (sin hat B)/[AC]`

but

`hat A + hat B + hat C = pi` and

`hat A = pi/3`
`hat B = pi/4`

so

`hat C = pi -pi/3-pi/4 = (5pi)/12`

and now

`BC= AB( (sin hat A)/(sin hat C)) = 6(sin(pi/3)/sin((5pi)/12))=`
`9sqrt2-3sqrt6`

and also

`AC = 6 (sin(pi/4)/sin((5pi)/12))=`
`6sqrt3-6`