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Common Core For Grade 8

Examples, videos, and solutions to help Grade 8 students learn how to use the Pythagorean theorem to determine missing side lengths of right triangles.

• Students use the Pythagorean theorem to determine missing side lengths of right triangles.

Lesson 16 Summary

The Pythagorean theorem can be used to find the unknown length of a leg of a right triangle.

An application of the Pythagorean theorem allows you to calculate the length of a diagonal of a rectangle, the distance between two points on the coordinate plane and the height that a ladder can reach as it leans against a wall.

Classwork

Exercises and Examples

Example 1

Pythagorean theorem as it applies to missing side lengths of triangles:

Given a right triangle with a hypotenuse with length units and a leg with length units, as shown, determine the length of the other leg.

Example 2

Pythagorean theorem as it applies to missing side lengths of triangles in a real-world problem:

• Suppose you have a ladder of length 13 feet. To make it sturdy enough to climb you must place the ladder exactly 5 feet from the wall of a building. You need to post a banner on the building 10 feet above the ground. Is the ladder long enough for you to reach the location you need to post the banner?

Example 3

Pythagorean theorem as it applies to missing side lengths of a right triangle:

• Given a right triangle with a hypotenuse of length 15 units and a leg of length 9, what is the length of the other leg?

Exercises

- Use the Pythagorean theorem to find the missing length of the leg in the right triangle.
- You have a 15-foot ladder and need to reach exactly 9 feet up the wall. How far away from the wall should you place the ladder so that you can reach your desired location?

Example 4

Pythagorean theorem as it applies to distances on a coordinate plane:

• We want to find the length of the segment AB on the coordinate plane, as shown.

Example 5

Pythagorean theorem as it applies to the length of a diagonal in a rectangle:

• Given a rectangle with side lengths of 8 cm and 2 cm, as shown, what is the length of the diagonal?

Exercises 3 - 6

3. Find the length of the segment AB.
4. Given a rectangle with dimensions 5 cm and 10 cm, as shown, find the length of the diagonal.
5. A right triangle has a hypotenuse of length 13 in and a leg with length 4 in. What is the length of the other leg?
6. Find the length of in the right triangle below.

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