Question

A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 2, respectively. The angle between A and C is `pi/4` and the angle between B and C is `pi/3`. What is the area of the triangle?

Answer 1

Area of triangle is `7.73` sq.unit

Explanation:

Angle between sides `A and C` is `/_b=pi/4=180/4=45^0`
Angle between sides `B and C` is `/_a=pi/3=180/3=60^0`
Angle between sides `A and B` is `/_c=180-(60+45)=75^0`

Now we know sides `A , B` and their included angle `/_c`

Sides `A= 8 , B=2, /_c=75^0`

Area of triangle is `A_t= (A*B*sinc)/2 = (8*cancel2*sin 75)/cancel2 = 8*sin75` or

`A_t ~~=7.73(2dp)`sq.unit

Area of triangle is `7.73(2dp)`sq.unit [Ans]