Question

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?

Answer 1

`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`