Question

A triangle has sides A, B, and C. If the angle between sides A and B is `(pi)/3`, the angle between sides B and C is `(5pi)/12`, and the length of B is 2, what is the area of the triangle?

Answer 1

Area of the triangle is `2.36(2dp)` sq units

Explanation:

The angle between sides A and B is `/_C=pi/3 = 180/3 = 60^0`
The angle between sides B and C is `/_A= (5pi)/12 = (5*180)/12= 75^0`
The angle between sides C and A is `/_B=180-(60+75) = 45^0`
`B=2` (given) Applying sine law we get `A/sinA=B/sinB or A=2*sin75/sin45=2.73` Now `A=2.73 ; B=2` and their included angle `/_C=60^0` So area of the triangle is `a*b*sinC/2= 2.73*2*sin60/2=2.36(2dp)`sq units [Ans}