A triangle has two corners with angles of # ( pi ) / 2 # and # ( pi )/ 6 #. If one side of the triangle has a length of #4 #, what is the largest possible area of the triangle?

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Answer 1 · 2018-02-07T08:14:06

Largest possible area of the right #Delta ABC = color(green)(~~ 13.8564)# sq units

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Three angles are #A = pi/2, B = pi/6, C = pi/3#

It is a right triangle with angles 30, 60, 90 and the sides will be in

the ratio of 1 : #sqrt3 # : 2

To get the largest are, side 4 should correspond to the least angle #pi/6#

Three sides will be #4, 4sqrt3, 8#

Largest possible area of the right #Delta ABC = (1/2) * 4 * 4sqrt3 color(green)(~~ 13.8564)# sq units