Is it a Right Triangle Calculator

Created by Kenneth Alambra
Reviewed by Purnima Singh, PhD
Last updated: May 30, 2022

This is it a right triangle calculator will help you determine whether or not a triangle qualifies to be a right triangle. This tool will be your companion when you just want to make sure you have a right triangle. In this right triangle calculator, you will learn:

  • What a right triangle is; and
  • How to figure out if a triangle is a right triangle using our calculator.

You're on the right track, so keep on reading.

What is a right triangle and how to tell if it is a right triangle?

A right triangle is a triangle with one of its interior angles equal to 90°, hence the name. Since a triangle has a total of 180° for its interior angles, if one of its angles is 90°, that means its two remaining interior angles have a total of 90°, too. So to check if a triangle is right, its two remaining angles need to be complementary and acute (since every complementary angle is acute). In equation form, we express that as:

α+β+90°=180°α+β=180°90°α+β=90°\begin{align*} \alpha + \beta + 90\degree &= 180\degree\\ \alpha + \beta &= 180\degree - 90\degree\\ \alpha + \beta &= 90\degree \end{align*}

where:

  • α\alpha and β\beta - Remaining angles of a right triangle that turn out to be complementary.

Aside from the relationship of the interior angles of a right triangle, its sides should also follow the Pythagorean theorem. That means that a right triangle has to have a hypotenuse, which we can denote as cc, which has a length equal to:

c=a2+b2c = \sqrt{a^2 + b^2}

where:

  • aa and bb - Sides of the triangle forming a right angle.

Lastly, we can observe the following trigonometric functions when dealing with right triangles:

For angle α\alpha:

sin(α)=accos(α)=bctan(α)=ab\begin{align*} &sin{(\alpha)} = \frac{a}{c}\\\\ &cos{(\alpha)} = \frac{b}{c}\\\\ &tan{(\alpha)} = \frac{a}{b} \end{align*}

For angle β\beta:

sin(β)=bccos(β)=actan(β)=ba\begin{align*} &sin{(\beta)} = \frac{b}{c}\\\\ &cos{(\beta)} = \frac{a}{c}\\\\ &tan{(\beta)} = \frac{b}{a} \end{align*}

Note that:

  • aa - Length of side opposite angle α\alpha;
  • bb - Length of side opposite angle β\beta; and
  • cc - Length of the hypotenuse, or the side opposite the 90° angle.

If a triangle fails to meet even one of these conditions, then that triangle is not a right triangle.

How to figure out if it is a right triangle - Calculator guide

You can check your triangle in three different ways depending on the known parameters of the triangle you have. To use our right triangle calculator:

  1. Choose in the Given selection your known set of parameters whether you know the 3 sides, angles α and β, or 2 sides and 1 angle.
  2. Skip this step if you choose any of the first two options. If you chose 2 sides and 1 angle, select among the options which sides and angle you know.
  3. Enter your known measurements depending on your selections.

After entering your last known parameter, our calculator will then display a message if your triangle is a right triangle or not.

Want to learn more about triangles? Here are our other triangle calculators you can explore:

FAQ

Is it possible to draw a right isosceles triangle?

Yes, it is possible. To draw a right isosceles triangle, make sure the sides forming the right angle have equal lengths. Then connect their ends to draw a hypotenuse to form a right isosceles triangle. Drawing a diagonal inside a square will also let you draw right isosceles triangles.

How do I tell if it is a right triangle?

To determine a right triangle, check if:

  1. One of its interior angles is equal to 90°.
  2. The sum of two of its angles is equal to 90°.
  3. Its longest side, say c, is equal to the square root of the sum of the square of the two shorter sides, say a and b. In equation form: c = √(a² + b²).
  4. It can meet any of these conditions:
  • sin(α) = a/c
  • cos(α) = b/c
  • tan(α) = a/b

where a is the side opposite angle α, b is the side adjacent to angle α, and c is the hypotenuse.

Kenneth Alambra
Given
3 sides
right triangle with sides a,b,c and angles α,β




a
in
b
in
c
in
Check out 17 similar triangle calculators 🔺
30 60 90 triangle45 45 90 triangleArea of a right triangle… 14 more
People also viewed…

BMR - Harris-Benedict equation

Harris-Benedict calculator uses one of the three most popular BMR formulas. Knowing your BMR (basal metabolic weight) may help you make important decisions about your diet and lifestyle.

Matrix determinant

The matrix determinant calculator is your fast and easy way to get the determinant of any square matrix of size 2x2, 3x3, or 4x4.

Simplifying radicals

The simplifying radicals calculator takes your expression containing roots and transforms it into the simplest radical form.

Steps to calories

Steps to calories calculator helps you to estimate the total amount to calories burned while walking.
Omni Calculator
Copyright by Omni Calculator sp. z o.o.
Privacy policy & cookies
main background