Mathematical Calculators

30 60 90 Triangle Calculator

With our 30 60 90 triangle calculator you can solve the special right triangle.

Visualization of special right triangle

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Table of contents

What is a 30 60 90 triangle?
30-60-90 is a special kind of triangle
Which side of 30 60 90 triangle is which?
How to solve the special right triangle?
Special right triangle ratio
With our 30 60 90 triangle calculator you can solve its hypotenuse, measurements and ratio. From this page you will also find more information of 30 60 90 calculator, which is many times referred as special right triangle.

What is a 30 60 90 triangle?

A 30 60 90 triangle is a special right triangle that has interior angles measuring 30°, 60°, and 90°. Because of this special form it is easy to calculate the rest of the dimensions if you know one of them!

30-60-90 is a special kind of triangle

A 30-60-90 right triangle is a special type of right triangle. 30 60 90 triangle's three angles measure 30 degrees, 60 degrees, and 90 degrees. The triangle is significant because the sides exist in an easy-to-remember ratio: 1√(3/2). This means that the hypotenuse is twice as long as the shorter leg and the longer leg is the square root of three times the shorter leg.

Which side of 30 60 90 triangle is which?

The side which is opposite to the 30 degree angle will always have the shortest length. The side opposite the 60 degree angle will be √3 times as long. The side opposite the 90 degree angle will be twice as long. Remember that the shortest opposite the smallest angle and the longest side will be opposite the largest angle.

How to solve the special right triangle?

Formulas for solving the special right triangle, or 30 60 90 triangle, are simple. You can find all the measurements easily if you know short leg, long leg or hypotenuse!
If we know the shorter leg length a, we can find out that:
b = a√3
c = 2a
If the longer leg length b is the one parameter given, then:
a = b√3/3
c = 2b√3/3
For hypotenuse c known, the legs formulas look as follows:
a = c/2
b = c√3/2
For area the formula looks the following:
area = (a²√3)/2
For calculating perimeter the formula looks the following:
perimeter = a + a√3 + 2a = a(3 + √3)

Special right triangle ratio

The rules for special right triangle are simple. It has one right angle and its sides are in easy relationship with each other.
ratio = a : a√3 : 2a.
Formula of special right triangle

John Cruz
Article author
John Cruz
John is a PhD student with a passion to mathematics and education. In his freetime John likes to go hiking and bicycling.

30 60 90 Triangle Calculator English
Published: Tue Jul 06 2021
In category Mathematical calculators
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