A triangle has sides A, B, and C. If the angle between sides A and B is #(5pi)/12#, the angle between sides B and C is #(5pi)/12#, and the length of B is 6, what is the area of the triangle?

1 Answer
Deepak G.
Aug 4, 2016

#=33.62#

Explanation:

Since the triangle is isosceles height divides the base equally.
In other words the said triangle consists of 2 right angled triangles with base=#B/2=6/2=3# and hypotenuse =Side #A#
Therefore we can write
#A(cos((5pi)/12))=3#
or
#A(0.2588)=3#
or
#A=3/0.2588#
or
#A=11.6#
In a right angled triangle height #h=sqrt(11.6^2-3^2)=11.21#
Therefore Area of the triangle#=1/2(h)(B)#
#=1/2(11.21)(6)#
#=(11.21)(3)#
#=33.62#

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