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 `(5pi)/24` and the angle between B and C is `(pi)/24`. What is the area of the triangle?

Answer 1

Area of the triangle is `1.06 sq.unit`

Explanation:

The angle between sides A & C is `/_b=5*180/24=37.5^0`
The angle between sides B & C is `/_a=180/24=7.5^0`
The included angle between sides A & B is `/_c=180-(37.5+7.5)=135^0` So we have `A=3 ; B=1` and included angle between them is `135^0`. Area of the triangle is `A_t=1/2*a*b*sinc=1/2*3*1*sin135=3/2*0.707=1.06 sq.unit`[Ans]