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 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 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 a right triangle?

Back

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

Front

How can the Pythagorean Theorem be used in real life?

Back

The Pythagorean Theorem can be used in various real-life situations, such as determining the distance between two points, calculating the height of a tree using its shadow, or in construction to ensure structures are level.

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-degree angle is the shortest, the side opposite the 60-degree angle is √3 times the shortest side, and the hypotenuse is twice 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

If a rectangular monitor is 30 cm wide and 24 cm high, what is its diagonal size?

Back

The diagonal size is 38 cm, calculated using the Pythagorean Theorem: c = √(30² + 24²) = √(900 + 576) = √1476 ≈ 38.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

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

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: if you know the lengths of two sides, rearrange the formula to solve for the missing side.