Question

A triangle has two corners with angles of `pi / 2` and `(3 pi )/ 8`. If one side of the triangle has a length of `12`, what is the largest possible area of the triangle?

Answer 1

Largest possible Area of Delta ABC = `A_t = color (red)(173.8236)`

Explanation:

`C = pi / 2, B = (3pi)/8, A = pi - pi/2 - (3pi)/8 = pi / 8`

Side 12 should correspond to the smallest angle (pi/8) to get the largest possible area.

`12 / sin (pi/8) = b / sin ((3pi) / 8) = c / sin (pi/2)`

`b = (12 * sin ((3pi)/8)) / sin (pi/8) = 28.9706`

`c = (12sin(pi/2)) / sin (pi/8) = 31.3575`

Largest possible area of Delta ABC = `A_t = (1/2) b a = (1/2) * 28.9706 * 12 = color (red)(173.8236)`