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A triangle has two corners with angles of # pi / 4 # and # pi / 2 #. If one side of the triangle has a length of #15 #, what is the largest possible area of the triangle?

Answer 1

Mason Adams

#A = 112.5#

Let #angle A = pi/4#

Let #angle B = pi/2#

Then #angle C = pi - pi/2 - pi/4#

#angle C = pi/4#

Please observe that is this is an isosceles right triangle. If we choose the side that is length 15 to be the side opposite #angle A#, then the side opposite #angle C# must also be length 15 and these sides are the base and the height of the right triangle. Therefore, the area is:

#A = 1/2(15)(15)#

#A = 112.5#

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Answer 2

Sophia Alfred

The largest possible area of the triangle is ( \frac{225}{2} ) square units.

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