A triangle has two corners with angles of $\frac{π}{2}$ $( pi ) / 2$ and $\frac{π}{6}$ $( pi )/ 6$ . If one side of the triangle has a length of $4$ $4$ , 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

A triangle has two corners with angles of ( pi ) / 2 π2 ( pi ) / 2 and ( pi )/ 6 π6 ( pi )/ 6 . If one side of the triangle has a length of 4 44 , what is the largest possible area of the triangle?