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: c² = a² + b².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

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

Back

Using the Pythagorean Theorem: c² = 6² + 8²; c² = 36 + 64; c² = 100; c = 10.

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 5 and 12, what is the length of the hypotenuse?

Back

c = √(5² + 12²) = √(25 + 144) = √169 = 13.

Front

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

Back

In a right triangle, the hypotenuse is always the longest side, opposite the right angle.

Front

If the hypotenuse of a right triangle is 15 and one leg is 9, what is the length of the other leg?

Back

Using the Pythagorean Theorem: 15² = 9² + b²; 225 = 81 + b²; b² = 144; b = 12.

Front

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

Back

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and angles.

Front

How can you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

If the squares of the lengths of the two shorter sides add up to the square of the length of the longest side, then the triangle is a right triangle.

Front

What is the length of the diagonal of a rectangle with a width of 8 inches and a height of 6 inches?

Back

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