A triangle has two corners with angles of $\frac{π}{4}$ $pi / 4$ and $\frac{π}{2}$ $pi / 2$ . If one side of the triangle has a length of $3$ $3$ , 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 $A_{t} = 4.5$ $A_t = color(green)(4.5$ sq. units

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

Third angle $ˆ C = π - \frac{π}{2} - \frac{π}{4} = \frac{π}{4}$ $hatC = pi - pi/2 - pi/4 = pi/4$

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 ( $\frac{π}{4}$ $pi/4$ , in this case).

Area of triangle $A_{t} = (\frac{1}{2}) b c$ $A_t = (1/2) b c$ where b = c = 3.

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

A triangle has two corners with angles of pi / 4 π4 pi / 4 and pi / 2 π2 pi / 2 . If one side of the triangle has a length of 3 33 , what is the largest possible area of the triangle?