Understanding 30-60-90 Triangles

30-60-90 triangles are really useful for finding heights in math problems.

These triangles have a special relationship between their sides:

• The shortest side, which is opposite the $30^\circ$ angle, is called $x$.
• The side opposite the $60^\circ$ angle is longer and is $x\sqrt{3}$.
• The longest side, which is opposite the right angle, is called the hypotenuse and is $2x$.

Let’s look at an example!

If you want to find the height of an equilateral triangle with each side measuring 6 units, you can cut it in half. This gives you two 30-60-90 triangles.

In this case, the height of the triangle becomes $x\sqrt{3} = 3\sqrt{3}$. This makes your math much easier!

By using what we know about 30-60-90 triangles, we can find heights in real-life situations, like in building design and construction.