Finding the Measurement of the Right Triangle's Leg using the Pythagorean Theorem

When given the lengths of two sides of a right triangle, the Pythagorean theorem allows you to find the length of the third side. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as:

Pythagorean Theorem Formula

a2 b2 c2

Step-by-Step Guide to Finding the Other Leg in a Right Triangle

Let's start with an example problem where one leg of the right triangle is 10 units and the hypotenuse is 15 units. We aim to find the length of the other leg.

Example 1

Identify the known values: One leg (a) 10 units Hypotenuse (c) 15 units Find the other leg (b).

102 b2 152

100 b2 225

b2 225 - 100

b2 125

b √125

b ≈ 11.18 units

Example 2: Hypotenuse (16) and Other Shorter Leg (9)

Given:

Hypotenuse (c) 16 units Other leg (b) 9 units

Use the Pythagorean theorem to find the missing leg:

162 92 b2

256 81 b2

b2 256 - 81

b2 175

b √175

b ≈ 13.22 units

General Steps

Identify the given values (a, b, or c). Substitute the values into the equation. Isolate the unknown by manipulating the equation. Solve for the unknown by taking the square root. Verify the result with a calculator if needed.

Conclusion

The Pythagorean theorem is a fundamental principle in geometry that helps solve real-world problems involving right triangles. By following a systematic approach, you can quickly and accurately determine the unknown side of a right triangle.

Further Reading

For more detailed information and practice problems, refer to the following resources:

Math Open Reference - Pythagoras Theorem Math is Fun - Pythagorean Theorem