A triangle has two corners with angles of # pi / 4 # and # pi / 2 #. If one side of the triangle has a length of #3 #, what is the largest possible area of the triangle?

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Answer 1 · 2018-02-12T09:29:30

Largest possible area of triangle #A_t = color(green)(4.5# sq. units

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Given #hatA = pi/2, hatB = pi / 4

Third angle #hatC = pi - pi/2 - pi/4 = pi/4#

It's a right isosceles triangle.

To get the largest area of the triangle, length 3 should be equated to the side opposite to the least angle (#pi/4#, in this case).

Area of triangle #A_t = (1/2) b c# where b = c = 3.

#:.# Largest possible area #A_t = (1/2) * 3 * 3 = 9/2 = color(green)(4.5# sq. units