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?

1 Answer
Binayaka C.
Feb 8, 2017

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]

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