Question

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

Answer 1

`A=1/2(2)(2sqrt3)=2sqrt3` sq units

Explanation:

There is a kind of triangle that in degree format is called a 30-60-90 triangle (and so would have angles of `pi/2, pi/3, pi/6`. The ratio of the sides of this kind of a triangle are 1, `sqrt3`, 2.

If we take the length of 2 and assign that to the shortest side, then we'll have sides of 2, `2sqrt3`, 4.

The area of a triangle is found by:

`A=1/2bh`

and so our triangle is:

`A=1/2(2)(2sqrt3)=2sqrt3` sq units