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

cm
cm
cm
cm²
cm

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?
Triangle calc, find a, find b
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.

Triangle calc, find a, find b

Triangles are a fundamental part of geometry and many algebraic formulas. However, it can be tricky to find the length of a side of a triangle when you know just one of the sides. In this blog post, we’ll show you how to find the length of a side of a triangle regardless of its orientation.

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
Add 30 60 90 Triangle Calculator to your own website

Other mathematical calculators

Vector Cross Product Calculator

Expected Value Calculator

Online Scientific Calculator

Standard Deviation Calculator

Percentage Calculator

Fractions Calculator

Pounds To Cups Converter: Flour, Sugar, Milk..

Circle Circumference Calculator

Double Angle Formula Calculator

Mathematical Root Calculator (square Root Calculator)

Triangle Area Calculator

Coterminal Angle Calculator

Dot Product Calculator

Midpoint Calculator

Significant Figures Converter (Sig Figs Calculator)

Arc Length Calculator For Circle

Point Estimate Calculator

Percentage Increase Calculator

Percentage Difference Calculator

Linear Interpolation Calculator

QR Decomposition Calculator

Matrix Transpose Calculator

Triangle Hypotenuse Calculator

Trigonometry Calculator

Right Triangle Side And Angle Calculator (triangle Calculator)

45 45 90 Triangle Calculator (right Triangle Calculator)

Matrix Multiply Calculator

Average Calculator

Random Number Generator

Margin Of Error Calculator

Angle Between Two Vectors Calculator

LCM Calculator - Least Common Multiple Calculator

Square Footage Calculator

Exponent Calculator (power Calculator)

Math Remainder Calculator

Rule Of Three Calculator - Direct Proportion

Quadratic Formula Calculator

Sum Calculator

Perimeter Calculator

Z Score Calculator (z Value)

Fibonacci Calculator

Capsule Volume Calculator

Pyramid Volume Calculator

Triangular Prism Volume Calculator

Rectangle Volume Calculator

Cone Volume Calculator

Cube Volume Calculator

Cylinder Volume Calculator

Scale Factor Dilation Calculator

Shannon Diversity Index Calculator

Bayes Theorem Calculator

Antilogarithm Calculator

Eˣ Calculator

Prime Number Calculator

Exponential Growth Calculator

Sample Size Calculator

Inverse Logarithm (log) Calculator

Poisson Distribution Calculator

Multiplicative Inverse Calculator

Marks Percentage Calculator

Ratio Calculator

Empirical Rule Calculator

P-value-calculator

Sphere Volume Calculator

NPV Calculator