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Home » Triangles » Pythagorean Theorem » Pythagorean Theorem: Lengths of Edges in a Right Triangle

Pythagorean Theorem: Lengths of Edges in a Right Triangle

Last updated: May 1, 2024 by Ido Sarig · This website generates income via ads and uses cookies · Terms of use · Privacy policy

Today we'll discuss one of the simple applications of the Pythagorean Theorem: finding the lengths of the edges in a right triangle.

The most common application of the Pythagorean theorem is to use the known lengths of two of the sides of a right triangle to find the length of the third side, using algebra and the formula a² + b² = c².

Right Triangle

Problem 1

In a right triangle, one of the legs (a) measures 4 units, the other leg (b) measures 3 units. Find the length of the hypotenuse, c.

Strategy

This is a straightforward application of the Pythagorean theorem. We know the lengths of sides a and b, so we simply plug these lengths into the formula a² + b² = c².

Solution

a= 4, b=3          //given
4² + 3² = c²        // simple substitution
16 + 9 = c²
25 =  c²
√25 = c
c = 5 //c is a side length, it must be positive, so we use only the positive root.

We can also use this formula to find the length of either one of the legs, if we know the length of the hypotenuse and the length of the other leg. For example:

Problem 2

In a right triangle, one of the legs (a) measures 12 units, the hypotenuse, c, measures 13 units. Find the length of the other leg (b)

Strategy

Just as we did above, since we know the lengths of side a and the hypotenuse c, we simply plug these lengths into the formula a² + b² = c².

Solution

a=12, c=13        //given
12² + b² = 13²        // substitution
144 + b² = 169
b² = 169-144=25 //rearranging
b= √25
b = 5 //b is a side length, it must be positive, so we use only the positive root.

« The Sum of Interior Angles in a Simple Convex Quadrangle
Finding the Area of an Isosceles Triangle »

About the Author

Ido Sarig is a high-tech executive with a BSc degree in Computer Engineering. His goal is to help you develop a better way to approach and solve geometry problems. You can contact him at [email protected].

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Welcome to Geometry Help! I'm Ido Sarig, a high-tech executive with a BSc degree in Computer Engineering and an MBA degree in Management of Technology. I'm here to tell you that geometry doesn't have to be so hard! My goal with this website is to help you develop a better way to approach and solve geometry problems, even if spatial awareness is not your strongest quality. Read More…

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