A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 7, respectively. The angle between A and C is (pi)/4 and the angle between B and C is (2pi)/3. What is the area of the triangle?

1 Answer
Jim G.
Feb 28, 2016

area ≈ 3.623 square units

Explanation:

To find the area of this triangle given sides A and B , use

" area " = 1/2 AB sintheta

where theta " is the angle between A and B"

The sum of the 3 angles in the triangle = pi

rArr theta = [pi - (pi/4 + (2pi)/3) ] = pi - (11pi)/12 = pi/12

" area " = 1/2 xx4 xx 7 xx sin(pi/12) ≈ 3.623" square units "

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