Question

A triangle has sides A, B, and C. The angle between sides A and B is `(5pi)/6`. If side C has a length of `24` and the angle between sides B and C is `pi/12`, what are the lengths of sides A and B?

Answer 1

The lengths of sides A and B are `12.42` each .

Explanation:

The angle between sides A and B is `/_C= 5*180/6=150^0`
The angle between sides B and C is `/_A= 180/12=15^0`
`:./_B= 180-(150+15)=15^0`.This is an isocelles triangle as two angles `/_A and/_B` are equal. Hence sides A and B are of equal length.
applying sine law we know `A/sinA=C/sinC or A=24*(sin15/sin150) =12.42 :. B=A=12.42`[Ans]