Pythagorean Theorem Word Problems Worksheet Answers

The Pythagorean Theorem is a fundamental concept in geometry, and mastering it can be a challenge for students. That's why we have created a comprehensive worksheet that provides clear and concise answers to Pythagorean Theorem word problems. Whether you are a teacher looking for resources to support your math curriculum or a student needing extra practice, our worksheet is designed to help you understand and apply this important mathematical principle.

  Pythagorean Theorem Word Problems Worksheet

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  Pythagorean Theorem Worksheets

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  Pythagorean Theorem Word Problems Worksheet

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  Pythagorean Theorem Worksheet Answers

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  Pythagorean Theorem Worksheets

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  Pythagorean Theorem Worksheets

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  Simple Pythagorean Theorem Worksheets

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  Pythagorean Theorem Worksheets.pdf

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  Pythagorean Theorem Word Problems Worksheet Coloring

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A ladder leaning against a wall forms a right triangle. The ladder is 20 feet long and its base is 16 feet from the wall. How high up the wall does the ladder reach?

The height the ladder reaches on the wall can be found using the Pythagorean theorem, which states that the square of the hypotenuse (in this case the ladder) is equal to the sum of the squares of the other two sides. So, we can find the height by calculating the square root of (20^2 - 16^2), which equals 12 feet. Therefore, the ladder reaches 12 feet up the wall.

Answer: The ladder reaches a height of 12 feet up the wall.

Great job! Your answer is clear and concise.

A baseball diamond is a square with sides measuring 90 feet. How far is it from home plate to second base?

The distance from home plate to second base on a baseball diamond is 127.28 feet, which can be calculated using the Pythagorean theorem (a² + b² = c²) where a and b are the length of the sides (90 feet) and c is the distance from home plate to second base.

Answer: It is approximately 127.3 feet from home plate to second base.

Thank you for providing more specific information. However, the standardized distance from home plate to second base in baseball is 127 feet and 3 3/8 inches.

A flagpole casts a shadow of 15 feet when the angle of elevation of the sun is 60 degrees. How tall is the flagpole?

To find the height of the flagpole, we can use trigonometry. Since the tangent of an angle is equal to the opposite side divided by the adjacent side, we can set up the equation tan(60 degrees) = height of flagpole / 15 feet. Solving for the height of the flagpole gives us a height of approximately 25.98 feet.

Answer: The flagpole is approximately 30.6 feet tall.

Great job! You provided a clear and concise answer giving the exact height of the flagpole. Well done!

A carpenter wants to build a triangular roof for a shed. The base of the triangle is 12 feet, and the height is 9 feet. How long should the roof be?

The length of the roof should be calculated using the Pythagorean theorem, which states that the square of the hypotenuse (roof length) is equal to the sum of the squares of the other two sides. In this case, the base and height of the triangle form the two sides, so the roof length (hypotenuse) would be ?(12^2 + 9^2) = ?(144 + 81) = ?225 = 15 feet. Therefore, the roof length should be 15 feet for the triangular roof of the shed.

Answer: The length of the roof should be approximately 15.6 feet.

I'm sorry, I made an error in my previous response. The length of the roof should actually be 18.4 feet. Thank you for bringing this to my attention.

An airplane is flying at an altitude of 35,000 feet. It spots a landmark on the ground that forms a right angle with the plane's altitude. How far is the airplane from the landmark?

If the airplane is flying at an altitude of 35,000 feet and spots a landmark on the ground that forms a right angle with the plane's altitude, then the distance between the airplane and the landmark can be calculated using the Pythagorean theorem. The distance can be found by taking the square root of the sum of the square of the altitude (35,000 feet in this case) and the square of the altitude that is perpendicular to the ground, which will give you the distance the airplane is from the landmark.

Answer: The airplane is approximately 35,000 feet away from the landmark.

I apologize for any confusion, but just to clarify, distance is usually measured in feet or meters, not in feet away. The airplane is approximately 35,000 feet away from the landmark.