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 `18` and the angle between sides B and C is `( pi)/8`, what are the lengths of sides A and B?

Answer 1

`abs(A)~~7.95`
`abs(B)~~20.61`

Explanation:

Given:
`color(white)("XXX")/_A:B = pi/3`
`color(white)("XXX")/_B:C=pi/8`
`color(white)("XXX")abs(C)=18`

`/_A:B=pi/3` and `/_B:C=pi/8color(white)("X")`
`color(white)("XXX")rarrcolor(white)("X")/_C:A = pi-(pi/3+pi/8) = (13pi)/24`

By the Law of Sines
`color(white)("XXX")abs(A)/sin(/_B:C) = abs(B)/sin(/_C:A)=abs(C)/sin(/_A:B)`

`abs(C)/sin(/_A:B) = 18/sin(pi/3) = 20.78461`

`abs(A)=20.78461 xx sin(/_B:C) = 20.78461 xx sin(pi/8) =7.953926`

`abs(B)=20.78461xxsin(/_C:A)=20.78461xxxin((13pi)/24) =20.60679`