Question

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

Answer 1

Area of triangle is `0.54 (2dp)` sq.unit.

Explanation:

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

The angle between sides `B and C` is `/_a= pi/2=180/2=90^0`

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

`B =2 ;` Appliying sine law we can find `A` as `A/sina=B/sinb or A =B* sina/sinb or A= 2* sin 90/sin 75 ~~2.07`

Now we know sides `A~~2.07 and B=2` and their included angle `/_c = 15^0`

Area of triangle `A_t= (A*B*sinc)/2 ~~ (2.07*2*sin15)/2 ~~ 0.54 (2dp)` sq.unit [Ans]