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 `14` and the angle between sides B and C is `(5pi)/12`, what are the lengths of sides A and B?

Answer 1

The length of the sides: `A=B=27.05(2dp)`

Explanation:

The angle between sides A and B is `/_C= pi/6=180/6=30^0`
The angle between sides B and C is `/_A= (5*pi)/12=5*180/12=75^0`
The angle between sides C and A is `/_B= 180-(30+75)=75^0`
C=14(given). We know `A/sinA=B/sinB=C/sinC :. A=C*sinA/sinC`
`:.A=14*sin75/sin30 =27.05(2dp)` Similarly `B=C*sinB/sinC :.B=14*sin75/sin30 =27.05(2dp)`