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

How do you find the length of the hypotenuse?

Back

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

Front

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

Back

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

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 the hypotenuse is 13 cm and one side is 5 cm, how do you find the other side?

Back

Use the formula: b = √(c² - a²). Here, b = √(13² - 5²) = √(169 - 25) = √144 = 12 cm.

Front

What is a right triangle?

Back

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

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle.

Front

If a right triangle has legs of lengths 9 cm and 12 cm, what is the length of the hypotenuse?

Back

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

Front

What is the formula to calculate the area of a right triangle?

Back

The area of a right triangle can be calculated using the formula: Area = (1/2) * base * height.

Front

If the area of a right triangle is 24 cm² and the base is 8 cm, what is the height?

Back

Using the area formula: 24 = (1/2) * 8 * height. Therefore, height = 24 / 4 = 6 cm.