Question

A triangle has sides A, B, and C. The angle between sides A and B is `(5pi)/12` and the angle between sides B and C is `pi/12`. If side B has a length of 33, what is the area of the triangle?

Answer 1

The area of triangle is `136.1 (1dp)` sq.unit

Explanation:

The angle between sides `A and B` is `/_c = (5pi)/12=(5*180)/12=75^0`

The angle between sides `B and C` is `/_a = pi/12=180/12=15^0`

The angle between sides `C and A` is `/_b = 180-(75+15)=90^0`

Applying sine law we can find `A/sina=B/sinb ; B=33 :. A/sin15=33/sin90 or A= 33*sin 15~~8.54(2 dp); [sin 90 =1]`

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

The area of triangle is `A_t =(A*B*sin c)/2= (8.54 * 33*sin 75)/2 ~~ 136.1(1dp)` sq.unit