# High School Math : How to find the height of an equilateral triangle

## Example Questions

### Example Question #481 : Geometry

An equilateral triangle has a side length of . What is the triangle's height ?

Not enough information to solve

Explanation:

The altitude, , divides the equilateral triangle into two  right triangles and divides the bottom side in half.

In a  right triangle, the sides of the triangle equal , and . In these equations  equals the length of the smallest side, which in our triangle is  or .

In this scenario:

and

Therefore,

### Example Question #1 : How To Find The Height Of An Equilateral Triangle

An equilateral triangle has a side length of .  What is its height, ?

Not enough information to solve

Explanation:

An altitude slices an equilateral triangle into two  triangles. These triangles follow a side-length pattern. The smallest of the two legs equals  and the hypotenuse equals . By way of the Pythagorean Theorem, the longest leg or .

Therefore, we can find the height of the altitude of this triangle by designating a value to . The hypotenuse of one of the  is also the side of the original equilateral triangle.  Therefore, one can say that  and .

### Example Question #2 : How To Find The Height Of An Equilateral Triangle

What is the height of an equilateral triangle with side 6?

Explanation:

When you draw the height in an equilateral triangle, it makes two 30-60-90 triangles. Because of that relationship, the height (which is across from the ) is

### Example Question #2 : How To Find The Height Of An Equilateral Triangle

Find the height of the following equilateral triangle:

Explanation:

Each angle in an equilateral triangle is .

Use the formula for  triangles in order to find the length of the height.

The formula is:

Where  is the length of the side opposite the

If we were to create a  triangle by drawing the height, the length of the side is , the base is , and the height is .

### Example Question #3 : How To Find The Height Of An Equilateral Triangle

Solve for the value of X in the following equilateral triangle:

Explanation:

If we draw a line segment between X and the base of the triangle, we form a  triangle.

We can use the relationships between the sides of a  triangle in order to find the length of X.

We know the base opposite the  is .

The value of the height opposite the must then be , or .

Therefore, the value of X will be twice the value of the height:

### Example Question #1 : How To Find The Height Of An Equilateral Triangle

What is the height of an equilateral triangle with a side length of 8 in?