A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 1, respectively. The angle between A and C is #(7pi)/24# and the angle between B and C is # (pi)/24#. What is the area of the triangle?

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Answer 1 · 2018-06-20T18:03:44

#A=5/2*sqrt(3)#

The third angle is given by
#pi/24+7pi/24+x=pi#
so #x=2/3+pi#
using the formula
#A=1/2*a*b*sin(gamma)#
we get

#A=5/2*sin(2/3*pi)#
so

#A=5/2*sqrt(3)#