A triangle has sides A, B, and C. The angle between sides A and B is #(5pi)/6# and the angle between sides B and C is #pi/12#. If side B has a length of 27, what is the area of the triangle?

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Answer 1 · 2016-02-21T05:53:26

Area #=182.25" " "#square units

We will take the side #b=27# as the base of the triangle
Angle #A=pi/12# and angle #C=(5pi)/6#

We need the height #h# to solve for the Area#=1/2bh#

Solve h

#b=h*cot A + h cot C#

#h=b/(cot A+cot C)#

#h=27/(cot (pi/12)+cot ((5pi)/6)#

#h=13.5#

Solve Area:

Area#=1/2 b h#

Area#=1/2(27)(13.5#

Area#=182.25" "#square units

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