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?

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Answer 1 · 2016-12-21T14:41:53

The area of the triangle is:

#S = 8*(2-sqrt3)#

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)#