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: a² + b² = c².

Front

In a right triangle with sides 6, 6.7, and 3, which side is the hypotenuse?

Back

The hypotenuse is the longest side of a right triangle. In this case, the hypotenuse is 6.7.

Front

If a ladder is 13 feet long and the base is 5 feet from the wall, how high does it reach on the wall?

Back

Using the Pythagorean Theorem: 5² + h² = 13². Solving gives h = 12 feet.

Front

An airplane flies 56 miles north and then 33 miles east. How far is it from the starting point?

Back

Using the Pythagorean Theorem: 56² + 33² = c². The distance from the starting point is 65 miles.

Front

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

Back

The formula is c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.

Front

If one side of a right triangle is 8 and the other is 6, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(8² + 6²) = √(64 + 36) = √100 = 10.

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 right triangle has a hypotenuse of 10 and one side of 6, what is the length of the other side?

Back

Using the Pythagorean Theorem: 6² + b² = 10². Solving gives b = 8.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

How can you determine if a triangle is a right triangle using side lengths?

Back

If the square of the longest side equals the sum of the squares of the other two sides, then it is a right triangle.