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 `14` and the angle between sides B and C is `( 3 pi)/8`, what are the lengths of sides A and B?

Answer 1

a= 14.94 ; b=12.83

Explanation:

The measurements as given in the question are depicted in the figure below

:

To determine sides 'a' and 'b', it is obvious that sine rule would be helpful here. Thus,
`sin A /a = sin B /b = Sin C/c`. Here A is`(3pi)/8`C is`pi/3` and B is `(pi-(3pi)/8- pi/3) = (7pi)/24`

`(sin ((3pi)/8))/a= (sin ((7pi)/24))/b= sin(pi/3)/14=sqrt3/28`

`0.9238/a =0.7933/b= 0.0618`

This gives a= 14.94 ; b=12.83