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 63, what is the area of the triangle?

1 Answer
Deepak G.
Aug 13, 2016

#=496.125#

Explanation:

Clearly this is a right-angled triangle since Angle between sides#A# and #C# is #=pi-((5pi)/12+pi/12)#
#=pi-pi/2#
#=pi/2#
In this right angled triangle side#A# is height and side #C# is base and side #B=63# is hypotenuse
#A=height=63sin(pi/12)# and
#C= base=63cos(pi/12)#
Therefore
Area of the triangle
#=1/2times height times base#
#=1/2times63sin(pi/12)times 63cos(pi/12)#
#=1/2times63(0.2588)times 63(0.966)#
#=496.125#

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