A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 5, respectively. The angle between A and C is #(7pi)/24# and the angle between B and C is # (3pi)/8#. What is the area of the triangle?

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Answer 1 · 2016-02-05T01:34:24

15.155

Given is Angle A=#(3pi)/8# and B=#(7pi)/24#, and side a =7, b =5
The angle between sides a and b would be C= #pi-(3pi)/8- (7pi)/24 =(2pi)/3#

The area of the triangle would be

#1/2 ab SinC # = #1/2# (35) Sin #(2pi)/3#

=#1/2#(35) sin #pi/3# = # 1/2 (35) sqrt3/2#= 15.155