Question

A triangle has sides A, B, and C. The angle between sides A and B is `(3pi)/4`. If side C has a length of `12` and the angle between sides B and C is `pi/12`, what are the lengths of sides A and B?

Answer 1

Lengths of sides `A` and `B` are `4.39(2dp) and 8.49(2dp)` unit .

Explanation:

The angle between sides `A` and `B` is `/_c= (3pi)/4= (3*180)/4=135^0`
The angle between sides `B` and `C` is `/_a= pi/12= 180/12=15^0`
The angle between sides `C` and `A` is `/_b= 180 -(135+15) =30^0`

Applying sine law we can find sides `A` and `B` as `A/sina=C/sinc or A = C * sin a/sin c = 12 * sin15/sin135 = 4.39(2dp)`.

Similarly,
`B/sinb=C/sinc or B = C * sin b/sin c = 12 * sin30/sin135 = 8.49(2dp)`.

Lengths of sides `A` and `B` are `4.39(2dp) and 8.49(2dp)` unit . [Ans]