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What is a Right Angle? - Definition & Formula

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  • 0:05 Definition of a Right Angle
  • 0:22 Notation
  • 1:15 Pythagorean Theorem
  • 2:53 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this lesson, you will learn about the properties that identify right angles. You will also discover where right angles can be found and learn about what makes them so useful. You can then test your knowledge with a quiz.

Definition of a Right Angle

A right angle is an angle that measures exactly 90 degrees. It is exactly a quarter of a circle. When you cut a pie into four equal pieces, the tip of each slice will form a right angle.

right angle

Notice how the tips of each slice make a corner that is a right angle.

Notation

Right angles have a special notation all their own. It is a symbol that makes it look like a little square is in the angle. It looks like this:

right angle

The little square box tells you that this angle is a right angle.

You will see right angles in many places. You will see them in squares and rectangles where each corner is a right angle. One of the most useful places you will see them is in triangles. When a triangle has a right angle, it becomes a special type of triangle called a right triangle. Right triangles always have exactly one angle that is 90 degrees. They look like this:

right angle

Right triangles provide the basis for many mathematical things, such as finding the distance up a slope if you only know the height of the hill and determining how wide the hill is. Without right triangles, we wouldn't have trigonometry. The trigonometric functions of sine, cosine, and tangent all are based on the right triangle.

Pythagorean Theorem

One of the most important formulas you will ever come across related to right triangles is the Pythagorean theorem. The Pythagorean theorem is the formula that relates all three sides of a right triangle to each other. It allows you to find one side given the other two.

right angle

The side c is always the hypotenuse or the side opposite the right angle. The hypotenuse is always the longest side of a right triangle. The Pythagorean theorem tells you that the hypotenuse squared is the same length as the sum of the squares of the other two sides.

Let's see how we can use the Pythagorean theorem to help us solve problems. Let's say we had this triangle, and we wanted to find the missing side.

right angle

The missing side is our hypotenuse, so we can label that side c. The side that is 3 can be labeled either a or b. We will label it a. The other side is then b. We can plug our information into the Pythagorean theorem to find our missing side like this:

right angle

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