Pythagorean Theorem

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: c² = a² + b².

Front

What is the formula to find the length of the hypotenuse in a right triangle?

Back

The formula to find the length of the hypotenuse (c) in a right triangle is: c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

How do you determine if a set of three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length is equal to the sum of the squares of the other two lengths. If a, b, and c are the lengths, then check if c² = a² + b².

Front

What is the relationship between the sides of a 5-12-13 triangle?

Back

The sides 5, 12, and 13 form a right triangle because 5² + 12² = 25 + 144 = 169, which is equal to 13².

Front

If one side of a right triangle is 40 km and the other is 75 km, how do you find the distance between the two points?

Back

Use the Pythagorean Theorem: c = √(40² + 75²) = √(1600 + 5625) = √7225 = 85 km.

Front

What is the square root of 25?

Back

The square root of 25 is 5.

Front

How do you calculate the distance between two points in a right triangle?

Back

To calculate the distance between two points in a right triangle, use the Pythagorean Theorem: c = √(a² + b²), where a and b are the lengths of the two sides.

Front

What is the height of a right triangle if one side is 12 feet and the hypotenuse is 20 feet?

Back

Using the Pythagorean Theorem: 20² = 12² + height², so 400 = 144 + height², thus height² = 256, and height = 16 feet.

Front

What is the distance a hummingbird needs to fly if its nest is 16 feet high and 12 feet away from the base of the tree?

Back

Use the Pythagorean Theorem: c = √(16² + 12²) = √(256 + 144) = √400 = 20 feet.

Front

What is the significance of the Pythagorean Theorem in real-world applications?

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The Pythagorean Theorem is used in various real-world applications, including construction, navigation, and physics, to calculate distances and relationships between points.