A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 4, respectively. The angle between A and C is #(7pi)/24# and the angle between B and C is # (13pi)/24#. What is the area of the triangle?

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Answer 1 · 2018-01-10T09:59:13

2

We know:
#rightarrow# angle #A=(13pi)/24#
#rightarrow# angle #B=(7pi)/24#

therefore we know angle #C = (4pi)/24 = pi/6# because the angles must sum to #pi#.

We also know:
#rightarrow# side #a=2#
#rightarrow# side #b=4#

So we know angle #C# and the sides adjacent to it, #a# and #b#. We can find the area using:

#Area=1/2a*b\*sin(C)#

#=1/2(2)(4)sin(pi/6) = 4sin(pi/6)#

since #sin(pi/6)=1/2#, we get:

Area #= 1/2(4)=2#