Pythagorean Theorem: Missing Sides

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 is a right triangle?

Back

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

Front

What are the sides of a right triangle called?

Back

The sides of a right triangle are called the legs (the two shorter sides) and the hypotenuse (the longest side opposite the right angle).

Front

If one leg of a right triangle is 3 units and the other leg is 4 units, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 3² + 4² = c²; 9 + 16 = c²; 25 = c²; c = 5 units.

Front

How do you find the length of a missing side in a right triangle?

Back

To find a missing side, use the Pythagorean Theorem: a² + b² = c². Rearrange the formula to solve for the missing side.

Front

What is the distance formula in relation to the Pythagorean Theorem?

Back

The distance formula, which calculates the distance between two points (x1, y1) and (x2, y2) in a coordinate plane, is derived from the Pythagorean Theorem: d = √((x2 - x1)² + (y2 - y1)²).

Front

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

Back

Use the Pythagorean Theorem: 6² + b² = 10²; 36 + b² = 100; b² = 64; b = 8 units.

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.

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?

Back

The Pythagorean Theorem can be used in various real-life situations, such as determining the height of a tree, the distance between two points, or the length of a ladder needed to reach a certain height.