A triangle has two corners with angles of $\frac{π}{4}$ $pi / 4$ and $\frac{π}{4}$ $pi / 4$ . If one side of the triangle has a length of $1$ $1$ , what is the largest possible area of the triangle?

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Answer 1 · 2018-01-24T09:17:38

Largest possible area of the triangle $Delta ABC = (1/2) * 1 * 1 = color (green)(0.5)$ sq. units

Three angles are $pi/4, pi/4, (pi-(pi/4 + pi/4)) = pi/2$

It’s an isosceles right triangle with sides in the ratio $1 : 1 : sqrt2$

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To get the largest possible area of the triangle, length ‘1’ should correspond to the smallest angle, viz. $pi/4$

Hence the sides are $1, 1, sqrt2$

Largest possible area of the triangle $Delta ABC = (1/2) * 1 * 1 = color (green)(0.5)$ sq. units

A triangle has two corners with angles of pi / 4 π4 pi / 4 and pi / 4 π4 pi / 4 . If one side of the triangle has a length of 1 11 , what is the largest possible area of the triangle?