Question

A triangle has two corners with angles of `( pi ) / 2` and `( 5 pi )/ 12`. If one side of the triangle has a length of `14`, what is the largest possible area of the triangle?

Answer 1

`color(blue)("Largest possible area of the right ") color(crimson)(Delta = 365.75 " sq units"`

Explanation:

Given `hat A = pi/2, hat B = (5pi)/12, hat C = pi - pi/2 - (5pi)/12 = pi/12`

To get the largest possible areaof the right triangle,

side 14 should correspond to the least angle `hat C = pi/12`

Applying the law of sines,

`a / sin A = b / sin b = c / sin C`

`b = (c * sin B) / sin C`

`b = (14 * sin ((5pi)/12)) / sin (pi/12) = 52.25`

Hence `"Largest possible area of right "`

`Delta = (1/2) * b * c = (1/2) * 14 * 52.25 = 365.75 " sq units"`