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/6. If side B has a length of 3, what is the area of the triangle?

1 Answer
Roella W.
Jan 7, 2016

2.25

Explanation:

Sketch
Area = 1/2*B*h (see sketch)
B = x+y
tan((5pi)/12) = h/x and tan(pi/6) = h/y = h/(B-x)
h = xtan((5pi)/12) = (B-x)tan(pi/6)
:. xtan((5pi)/12) +xtan(pi/6) = 3tan(pi/6)
x = (3tan(pi/6))/(tan((5pi)/12) + tan(pi/6))
:. h = tan((5pi)/12)*(3tan(pi/6))/(tan((5pi)/12) + tan(pi/6))
~~ (3.73*3*0.577)/(3.73 +0.577)
~~6.46/4.31 = 1.5
Area =0.5*3*1.5 = 2.25

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