Apply Pythagorean Theorem

Videos, examples, solutions, and lessons to help Grade 8 students learn how to apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Common Core: 8.G.7

Suggested Learning Targets

• I can recall the Pythagorean Theorem and its converse in order to apply it to real-world and mathematical problems (2 and 3 dimensional).
• I can solve basic mathematical Pythagorean Theorem problems and its converse
  to find missing length of sides of triangles in two and there-dimensions.
• I can apply Pythagorean Theorem in solving real-world problems dealing with two and three-dimensional shapes.

Prove and apply the Pythagorean Theorem to determine unknown side lengths in right-triangles 8.G.7

Using the Pythagorean Theorem
Examples:

1. A right triangle has one leg with length 3.2 and a hypotenuse with length 4.2. What is the length of the other leg?
2. Alfredo is a firefighter saving a cat trapped at the top of a vertical tree. She leans a 10 meter ladder against the tree, touching exactly the cat’s position. The base of the ladder is 3.1 meters from the tree. How high is the cat?

Applications of the Pythagorean Theorem
How to use the Pythagorean Theorem to solve real world problems?
Examples:

1. Jim and Eileen decided to take a shortcut through the woods to go to their friend’s house. When they went home they decided to take the long way around the woods to avoid getting muddy shoes. What total distance did they walk to and from their friend’s house?
2. Shari went to a level field to fly a kite. She let out all 650 feet of the string and tied it to a dstake. Then she walked out on the field until she was directly under the kite, which was 600 feet from the stake. How high was the kite from the ground?

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Apply the Pythagorean Theorem

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Applying Pythagorean Theorem
Example:
A soccer field is rectangular with a width of 60 yards and a length of 100 yards. The diagonal of the field is found by connecting a line from corner to corner inside the rectangle. To the nearest foot, how long is this diagonal?

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Applying the Pythagorean Theorem

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Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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