A triangle has sides A,B, and C. If the angle between sides A and B is (pi)/2, the angle between sides B and C is pi/12, and the length of B is 4, what is the area of the triangle?

1 Answer
Dec 21, 2016

The area of the triangle is:

S = 8*(2-sqrt3)

Explanation:

This is a right triangle, where A and B are the legs, and C the hypotenuse.

In a right triangle the ratio between the legs equals the tangent of the angle opposite the leg at the numerator, so that we have:

A/B= tan(pi/12)

or:

A = Btan(pi/12) = 4(2-sqrt(3))

And the area is:

S =1/2 A*B = 8*(2-sqrt3)