Pythagorean Theorem Word Problems Worksheet

Are you a math teacher or a student in need of practice with Pythagorean theorem word problems? Look no further than our Pythagorean Theorem Word Problems Worksheet! This worksheet is designed specifically for students who are studying or reviewing the Pythagorean theorem and need extra practice solving real-world applications. It provides a variety of word problems that require students to apply the theorem to determine unknown side lengths in right triangles.

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A ladder is leaning against a wall. If the bottom of the ladder is 5 feet away from the wall and the ladder is 12 feet long, how high up the wall does the ladder reach?

The ladder will reach a height of 11 feet up the wall. This can be calculated using the Pythagorean theorem where the sum of the squares of the two shorter sides (5 feet and the height) is equal to the square of the longest side (12 feet). Squaring 5 gives 25, and squaring 12 gives 144. When 25 is subtracted from 144, the square root of 119 is approximately 11 feet, which is the height the ladder reaches up the wall.

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

It is 127.3 feet from home plate to second base on a standard baseball diamond, based on the geometry of a right triangle formed by the two sides of the square.

A building has a rectangular footprint measuring 100 feet by 150 feet. How long is the diagonal across the building?

To find the length of the diagonal across the building, we can use the Pythagorean theorem, which states that the square of the length of the diagonal is equal to the sum of the squares of the two sides. In this case, the diagonal length can be calculated as the square root of (100^2 + 150^2), giving us a diagonal length of approximately 182.57 feet.

A ramp at a skate park has a horizontal length of 30 feet and a vertical rise of 20 feet. What is the length of the ramp?

Using the Pythagorean theorem, the length of the ramp can be calculated as the square root of the sum of the squares of the horizontal length and vertical rise. In this case, the length of the ramp is ?(30^2 + 20^2) = ?(900 + 400) = ?1300, which simplifies to approximately 36.06 feet.

A farmer wants to build a wire fence in the shape of a right triangle. If one leg of the triangle is 6 feet and the hypotenuse is 10 feet, what is the length of the other leg?

The length of the other leg of the right triangle can be found using the Pythagorean theorem, where the square of the hypotenuse (10 feet) equals the sum of the squares of the two legs. Therefore, the length of the other leg would be ?(10^2 - 6^2) = ?(100 - 36) = ?64 = 8 feet. Hence, the length of the other leg of the triangle is 8 feet.

A flagpole casts a shadow that is 15 feet long. If the angle of elevation from the tip of the shadow to the top of the flagpole is 60 degrees, how tall is the flagpole?

To find the height of the flagpole, we can use trigonometry. Since the angle of elevation is 60 degrees, we can use the tangent function, tan(60) = height/15. Solving for the height, we get height = 15 * tan(60) ? 25.98 feet. Therefore, the flagpole is approximately 25.98 feet tall.

A ladder is propped against a tree. The base of the tree is 8 feet away from the ladder, and the ladder reaches a height of 10 feet on the tree. What is the length of the ladder?

The length of the ladder can be calculated using the Pythagorean theorem, which states that the square of the length of the hypotenuse (the ladder in this case) is equal to the sum of the squares of the other two sides. So, in this scenario, the length of the ladder would be ?(8^2 + 10^2) = ?(64 + 100) = ?164 ? 12.8 feet.

A rectangular garden measures 20 feet by 30 feet. How long is the diagonal across the garden?

To find the length of the diagonal across the garden, you can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (diagonal) of a right triangle is equal to the sum of the squares of the other two sides. In this case, the diagonal is the hypotenuse, and the sides of the rectangle are the other two sides. So, the length of the diagonal is calculated as the square root of (20² + 30²), which is approximately 36.06 feet.

A basketball player is standing 15 feet away from the hoop. If the angle of elevation from the player to the rim is 30 degrees, how high is the rim?

To find the height of the rim, we use basic trigonometry. Given that the player is 15 feet away from the hoop and the angle of elevation is 30 degrees, we can use the tangent function. tan(30 degrees) = opposite side (height of the rim) / adjacent side (distance to the hoop). Therefore, the height of the rim = 15 feet * tan(30 degrees) ? 7.5 feet. So, the rim is approximately 7.5 feet high.

A set of stairs has a landing in the middle. The rise of each step is 7 inches, and there are 12 steps. How wide is the landing?

The landing on the stairs is 7 inches wide, as the rise of each step is 7 inches, and there are 12 steps on the stairs.