Amy has a master's degree in secondary education and has taught math at a public charter high school.
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.
Notice how the tips of each slice make a corner that is a right angle.
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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:
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 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.
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.
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.
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:
We've used our algebra skills to isolate the x variable to solve for it and to find our answer. After going through the process we see that our hypotenuse is 5.
If we were given the hypotenuse and one of the sides and asked to find the other side, what do we do?
We will start the same as we did before. We label our 5 as c because that is the hypotenuse. The 4 side we will label b and side x we will label a. We then plug our information into the Pythagorean theorem and solve for x.
We are still using our algebra skills to solve for x. This time we had to move our b to the other side by subtracting it. Our answer turns out to be 3.
Right angles are defined as those angles that measure exactly 90 degrees. The most important place you will see them is in triangles. The formula that comes from the right triangle is the Pythagorean theorem that relates all the sides of the right triangle to each other. The Pythagorean theorem tells you that the hypotenuse squared is the same length as the sum of the squares of the other two sides.
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What is a Right Angle? - Definition & Formula
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