A triangle has sides A,B, and C. If the angle between sides A and B is #(7pi)/12#, the angle between sides B and C is #pi/6#, and the length of B is 5, what is the area of the triangle?

1 Answer
Leland Adriano Alejandro
Jan 22, 2016

Area=#8.53766# square units

Explanation:

From the given, two angles #A=pi/6#, #C=(7pi)/12# and included side #b=5#. Try drawing the triangle. See that angle #B=pi/4# by computation using the formula #A+B+C=pi#. Also , the altitude from angle C to side c can be called height # h# is #h = b*sin (pi/6)=2.5#
Side #c# can be computed using formula #c=b*cos A+h*cot B#.
#c=5*cos (pi/6)+2.5*cot (pi/4)#=#2.5*(sqrt3+1)#

#c=2.5(sqrt3+1)#
Area can now be computed

Area#=1/2*b*c*sin A#

Area#=1/2*5*(2.5(sqrt3+1))*sin (pi/6)#

Area#=8.53766# square units

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