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 and the other side is 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 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 side opposite the 30° angle is the shortest.

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 do you find a missing side in a right triangle?

Back

To find a missing side, rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a², depending on which side is missing.

Front

What is the value of the hypotenuse if the two other sides are 6 and 8?

Back

c = √(6² + 8²) = √(36 + 64) = √100 = 10.

Front

If the hypotenuse is 10 and one side is 6, what is the length of the other side?

Back

Using the Pythagorean Theorem: b = √(10² - 6²) = √(100 - 36) = √64 = 8.

Front

What is a right triangle?

Back

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

Front

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

Back

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