Question

A triangle has sides A, B, and C. Sides A and B have lengths of 1 and 5, respectively. The angle between A and C is `(7pi)/24` and the angle between B and C is `(5pi)/24`. What is the area of the triangle?

Answer 1

The area of the triangle is `2.5` sq.unit

Explanation:

The angle between sides `A and C` is `/_b=(7pi)/24=52.5^0`
The angle between sides `B and C` is `/_a=(5pi)/24=37.5^0`
The angle between sides `A and B` is `/_c=180-(52.5+37.5)= 90^0`
The area of the triangle with sides `A=1 , B=5` and their included angle `/_c=90^0` is `A_t=(a*b*sinc)/2 = (1*5*sin90)/2=5/2=2.5 sq.unit`[Ans]