When do i use pythagorean theorem

The Pythagorean Theorem describes the lengths of the sides of a right triangle in a way that is so elegant and practical that the theorem is still widely used today. The theorem states that for any right triangle, the sum of the squares of the non-hypotenuse sides is equal to the square of the hypotenuse. The Pythagorean Theorem is one of the fundamental pillars of basic geometry, having countless practical applications - using the theorem, for instance, it's easy to find the distance between two points on a coordinate plane.

To use the Pythagorean Theorem on a triangle with a degree angle, label the shorter sides of the triangle a and b, and the longer side opposite of the right angle should be labelled c. As long as you know the length of two of the sides, you can solve for the third side by using the formula a squared plus b squared equals c squared. Place your known values into the equation and solve for the unknown variable, then take the square root of both sides of the equation to get the result.

If you want to use the Pythagorean Theorem to find the distance between 2 points, keep reading the article! Did this summary help you? Yes No. Log in Social login does not work in incognito and private browsers. Please log in with your username or email to continue. No account yet? Create an account. Edit this Article. We use cookies to make wikiHow great.

By using our site, you agree to our cookie policy. Cookie Settings. Learn why people trust wikiHow. Download Article Explore this Article methods. Tips and Warnings. Related Articles. Article Summary. Method 1. Ensure that your triangle is a right triangle. The Pythagorean Theorem is applicable only to right triangles, so, before proceeding, it's important to make sure your triangle fits the definition of a right triangle.

Luckily, there is only one qualifying factor - to be a right triangle, your triangle must contain one angle of exactly 90 degrees. Look for this special mark in one of the corners of your triangle. Assign the variables a, b, and c to the sides of your triangle.

In the Pythagorean Theorem, the variables a and b refer to the sides that meet in a right angle, while the variable c refers to the hypotenuse - the longest side which is always opposite the right angle.

So, to begin, assign the shorter sides of your triangle the variables a and b it doesn't matter which side is labeled 'a' or 'b' , and assign the hypotenuse the variable c. Determine which side s of the triangle you are solving for. The Pythagorean Theorem allows mathematicians to find the length of any one of a right triangle's sides as long as they know the lengths of the other two sides.

If the length of only one of your sides is unknown, you're ready to proceed. In this case, we know we're solving for the length of the third side, and, because we know the lengths of the other two, we're ready to go!

We'll return to this example problem in the following steps. If the lengths of two of your sides are unknown, you'll need to determine the length of one more side to use the Pythagorean Theorem. Basic trigonometry functions can help you here if you know one of the non-right angles in the triangle. Using the formula, you find that the length of c , the hypotenuse, is In this case, you did not know the value of c —you were given the square of the length of the hypotenuse, and had to figure it out from there.

When you are given an equation like and are asked to find the value of c , this is called finding the square root of a number. Notice you found a number, c , whose square was Finding a square root takes some practice, but it also takes knowledge of multiplication, division, and a little bit of trial and error.

Look at the table below. Number x. Number y which, when multiplied by itself, equals number x. Square root y. If you can remember those square numbers—or if you can use a calculator to find them—then finding many common square roots will be just a matter of recall. For which of these triangles is? This is not a right triangle, so you cannot use the Pythagorean Theorem to find r. The correct answer is Triangle B. This is a right triangle; when you sum the squares of the lengths of the sides, you get the square of the length of the hypotenuse.

Finding the Length of a Leg. Consider the example below. Find the length of side a in the triangle below. Use a calculator to estimate the square root to one decimal place. In this right triangle, you are given the measurements for the hypotenuse, c , and one leg, b.

The hypotenuse is always opposite the right angle and it is always the longest side of the triangle. To find the length of leg a , substitute the known values into the Pythagorean Theorem. Solve for a 2. Think: what number, when added to 36, gives you 49? The same principles can be used for air navigation. For instance, a plane can use its height above the ground and its distance from the destination airport to find the correct place to begin a descent to that airport.

Surveying is the process by which cartographers calculate the numerical distances and heights between different points before creating a map. Because terrain is often uneven, surveyors must find ways to take measurements of distance in a systematic way.

The Pythagorean Theorem is used to calculate the steepness of slopes of hills or mountains. A surveyor looks through a telescope toward a measuring stick a fixed distance away, so that the telescope's line of sight and the measuring stick form a right angle. Since the surveyor knows both the height of the measuring stick and the horizontal distance of the stick from the telescope, he can then use the theorem to find the length of the slope that covers that distance, and from that length, determine how steep it is.

Jon Zamboni began writing professionally in He has previously written for The Spiritual Herald, an urban health care and religious issues newspaper based in New York City, and online music magazine eBurban. The hypotenuse is red in the diagram below:. Practice Problems. Find the length of X. Show Answer. Step 2 Substitute values into the formula remember 'C' is the hypotenuse. Next step.

Step 3 Solve for the unknown. Popular pages mathwarehouse. Surface area of a Cylinder. Unit Circle Game.