Question

Triangle MNO is an equilateral triangle with sides measuring 16 square root of 3 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
$8 \sqrt{3} \times \sqrt{3} = 24$
the height is 24 .

Answer 2

Answer:

The height of the triangle is 24 units.

Step-by-step explanation:

The height of the given triangle is NR

Using the Pythagorean Theorem,

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

From the diagram, $|ON|=16\sqrt{3}$ units

and

$|OR|=\frac{1}{2}\times 16\sqrt{3}$

$|OR|=8\sqrt{3}$ units.

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

$|NR|^2+(8\sqrt{3})^2=(16\sqrt{3})^2$

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,

$NR=\sqrt{576}$

$NR=24$

Therefore the height of the triangle is 24 units.