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 is the formula to find the length of the hypotenuse?

Back

To find the length of the hypotenuse (c) in a right triangle, use the formula: c = √(a² + b²).

Front

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

Back

The length of the hypotenuse is 5 cm, calculated as c = √(3² + 4²) = √(9 + 16) = √25 = 5.

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

Back

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

Front

If the hypotenuse is 10 cm and one side is 6 cm, how do you find the other side?

Back

Use the formula: b = √(c² - a²). Here, b = √(10² - 6²) = √(100 - 36) = √64 = 8 cm.

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle and is opposite the right angle.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by: d = √((x2 - x1)² + (y2 - y1)²).

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 ladder against a wall or the distance between two points on a map.