A triangle has sides A, B, and C. The angle between sides A and B is (pi)/2 and the angle between sides B and C is pi/12. If side B has a length of 12, what is the area of the triangle?

1 Answer
Rui D.
Dec 30, 2015

Area = S = 19.292

Explanation:

If the angle between A and B is pi/2 then the triangle is a right one and its area is:
S = (A*B)/2

Since the angle between B and C is known and the length of B also is known, we can find A in this way:
tan (pi/12) = ("opposed cathetus")/("adjacent cathetus")
So tan (pi/12) = A/B => A = B*tan(pi/12)

Finally,
S = (B^2*tan(pi/12))/2
S = (12^2*0.267949)/2 = 19.292

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