A triangle has sides A, B, and C. The angle between sides A and B is pi/12 and the angle between sides B and C is pi/12. If side B has a length of 17, what is the area of the triangle?

1 Answer
Sep 30, 2017

The area of the triangle is 19.36 sq.unit [Ans]

Explanation:

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

Angle between sides B and C is /_a=pi/12=180/12=15^0

Angle between sides C and A is /_b=(180-(15+15)=150^0

The Law of Sines (or Sine Rule) is: A/sin a = B/sin b = C/sin c

B=17 :. A/sin a = B/sin b or A /sin15 = 17/sin150 or

A = 17* sin15/sin150 ~~ 8.8 So the sides A and B and their

included angle are A=8.8 , B=17 and /_c =15^0

The area of triangle is A_t= (A*B*sinc)/2 =(8.8*17*sin15)/2 or

A_t ~~19.36 sq.unit [Ans]