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What Is a Right Angle, and Why Is It Important?

If you’ve heard the term “right angle” in geometry class and wondered, “What is a right angle?” you’ve come to the right place. Here, we’ll define right angles, their properties, how they form, and how they convert to radians.

First, let’s define a right angle. In trigonometry, different types of angles are defined by their angle measurements. A right angle is 90 degrees. An acute angle is less than 90 degrees. An obtuse angle is more than 90 degrees.

Names for Different Triangles

Knowing how to classify your angles also helps you identify different triangles.

A right triangle is any triangle that contains a 90-degree angle while an obtuse triangle is a triangle with an obtuse angle. An acute triangle is a triangle with three acute angles.

what is a right angle: Diagram of three different triangles

If this has you curious about types of triangles, here’s what you need to know. Names for triangles are based on the length of their sides. For example, a triangle with all three different side lengths is called a scalene triangle. A triangle with two sides of equivalent length is called an isosceles triangle. Lastly, a triangle with three sides of equal length is called an equilateral triangle.

Special Properties for Right-Angled Triangles

A famous postulate named after Pythagoras, a Greek mathematician, tells us how the two legs of a right triangle relate to its hypotenuse, or the triangle’s longest side. The Pythagorean Theorem says the sum of the squares of the side lengths of a right-angled triangle is always equal to the square of the hypotenuse.

what is a right angle: A right-angled triangle

Right Angles Are Formed by Perpendicular Lines

Perpendicular lines, or straight lines that intersect each other at a 90-degree angle, create right angles. Knowing what makes a right angle helps you often, like when drawing a line segment like the one below.

Triangle with a line segment showing the right angle

What’s a Right Angle in Radians?

Degrees are the most common unit of measure for angles in a polygon. Sometimes, if you are working with trigonometric functions like sine or cosine, the calculation is easier if you convert to a different unit of measure, the radian.

Radians are measured in units of pi. Pi radians equal 180 degrees. Therefore, a right angle is equal to Pi divided by two radians, which is 90 degrees.

Why Do Right Angles Matter?

Right angles are everywhere, from your coffee table to the roads in your city. A triangle that has a right angle is also known as a right triangle, to which you can apply special properties such as the Pythagorean Theorem. Right angles are important to recognize and to understand, since they’re used everywhere from geometry to trigonometry to real-life applications.

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