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 8, what is the area of the triangle?

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Answer 1 · 2016-01-28T11:24:52

#Area=8# square units

Use #Area=1/2*b*h#

Compute height #h#. The altitude from angle #B# to side #b#

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

#h=8/(cot (pi/12)+cot (5pi/12))=2#

#h=2#

Compute Area:

#Area =1/2*8*2#

#Area = 8#