Pythagorean Theorem - Finding the hypotenuse

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: a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

If one side of a right triangle is 8 and the other side is 13, how do you find the hypotenuse?

Back

Use the Pythagorean Theorem: c² = 8² + 13². Calculate c = √(64 + 169) = √233.

Front

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

Back

The formula to find the hypotenuse is c = √(a² + b²).

Front

In a right triangle, if the lengths of the two legs are 6 and 8, what is the length of the hypotenuse?

Back

c = √(6² + 8²) = √(36 + 64) = √100 = 10.

Front

What is the length of the diagonal of a rectangle with a width of 8 inches and a height of 11 inches?

Back

Use the Pythagorean Theorem: c = √(8² + 11²) = √(64 + 121) = √185 ≈ 13.6 inches.

Front

If the hypotenuse of a right triangle is 10 and one leg is 6, how do you find the other leg?

Back

Use the formula: b = √(c² - a²). Here, b = √(10² - 6²) = √(100 - 36) = √64 = 8.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

If a triangle has sides of lengths 5, 12, and 13, is it a right triangle?

Back

Yes, because 5² + 12² = 25 + 144 = 169 = 13².

Front

What is the hypotenuse of a right triangle with legs measuring 9 and 12?

Back

c = √(9² + 12²) = √(81 + 144) = √225 = 15.