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

Answer 1

`A=15.45` units and `B= 15.45` Units

Explanation:

The opposite angle of side A is `5*180/12=75^0` ; The opposite angle of side C is `180/6=30^0`;The opposite angle of side A is `:.180-75-30=105^0`;
Using sine law we get `A/sinA=C/sinC or A= 8 * (sin75/sin30)=15.45`; `B=15.45` since this is an isocelles triangle We also get `B/sinB=C/sinC or B= 8 * (sin75/sin30)=15.45`;[Ans]