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?

1 Answer
May 23, 2017

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]