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?

1 Answer
Apr 1, 2018

#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"#