Question

Triangle MNO is an equilateral triangle with sides measuring 16 square root of 3 units.

What is the height of the triangle?
NR units

Answer 1

M.N and O are 60 degree. And you have to know that 30 60 and 90 triangle. if 30 degrees opposite is measuring A , 60 is A square root 3 and the 90's opposite is being 2A. So 90 degree opposite is 16 square root 3 and 30 degree is being 8 square root 3 and 60 is

`8 √(3) * √(3) = 24`
the height is 24 .

Answer 2

The height of the triangle is 24 units.

Explanation:

The height of the given triangle is NR

Using the Pythagorean Theorem,

`|NR|^2+|OR|^2=|ON|^2`

From the diagram,
`|ON|=16√(3)` units

and

`|OR|=(1)/(2)* 16√(3)`

`|OR|=8√(3)` units.

We substitute all these values into the above formula to get,

`|NR|^2+(8√(3))^2=(16√(3))^2`

We evaluate to get,

`|NR|^2+64(3)=256(3)`

We group like terms to get,

`|NR|^2=256(3)-64(3)`

`|NR|^2=3(256-64)`

`|NR|^2=3(192)`

`|NR|^2=576`

We take the positive square root of both sides to get,

`NR=√(576)`

`NR=24`

Therefore the height of the triangle is 24 units.