Question

A triangle has sides A, B, and C. Sides A and B have lengths of 3 and 1, respectively. The angle between A and C is `(3pi)/8` and the angle between B and C is `(5pi)/12`. What is the area of the triangle?

Answer 1

The area of the triangle is `0.91 (2dp)` sq.unit

Explanation:

The angle between sides A and C is `/_b = (3pi)/8 = (3*180)/8 = 67.5^0`
The angle between sides B and C is `/_a = (5pi)/12 = (5*180)/12 = 75^0`
The angle between sides A and B is `/_c = 180-(67.5+75) = 37.5^0`

So , the two sides and their included angle is known as `A=3 , B=1 , /_c =37.5^0`

The area of the triangle is `A_t = (A*B*sinc)/2 = (3 * 1 * sin37.5)/2 ~~ 0.91 (2dp)` sq.unit [Ans]