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 are the components of a right triangle?

Back

A right triangle consists of three sides: the hypotenuse (the longest side opposite the right angle), and the two legs (the sides that form the right angle).

Front

How do you find the length of the hypotenuse using the Pythagorean Theorem?

Back

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

Front

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

Back

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

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. The shortest side is opposite the 30-degree angle, the longer leg is opposite the 60-degree angle, and the hypotenuse is twice the length of the shortest side.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

How can the Pythagorean Theorem be applied in real-life situations?

Back

The Pythagorean Theorem can be used in various real-life situations, such as determining the height of a ladder needed to reach a certain height when placed a certain distance away from a wall.

Front

What is the formula to find the length of one leg of a right triangle if the hypotenuse and the other leg are known?

Back

If the hypotenuse (c) and one leg (a) are known, the length of the other leg (b) can be found using the formula b = √(c² - a²).

Front

In a right triangle, if one leg is 12 and the hypotenuse is 13, what is the length of the other leg?

Back

Using the formula b = √(c² - a²): b = √(13² - 12²) = √(169 - 144) = √25 = 5.

Front

What is the significance of the Pythagorean Theorem in geometry?

Back

The Pythagorean Theorem is fundamental in geometry as it establishes a relationship between the sides of right triangles, which is essential for solving various geometric problems.