Pythagorean Thm

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 in a right triangle?

Back

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

Front

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

Back

The length of the hypotenuse is 5 units, 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 side opposite the 30° angle is the shortest, the side opposite the 60° angle is √3 times the shortest side, and the hypotenuse is twice the shortest side.

Front

What is the distance formula used to find the distance between two points (x1, y1) and (x2, y2) in a coordinate plane?

Back

The distance formula is: d = √((x2 - x1)² + (y2 - y1)²).

Front

If a right triangle has legs of lengths 6 and 8, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 10 units, calculated as: c = √(6² + 8²) = √(36 + 64) = √100 = 10.

Front

What is the area of a right triangle with a base of 5 units and a height of 12 units?

Back

The area of the triangle is 30 square units, calculated as: Area = (1/2) * base * height = (1/2) * 5 * 12 = 30.

Front

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

Back

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

Front

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

Back

The Pythagorean Theorem is used in various real-life applications such as construction, navigation, and physics to determine distances and relationships between different points.

Front

If the hypotenuse of a right triangle is 13 units and one leg is 5 units, what is the length of the other leg?

Back

The length of the other leg is 12 units, calculated as: b = √(c² - a²) = √(13² - 5²) = √(169 - 25) = √144 = 12.