Applying the 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: a² + b² = c².

Front

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

Back

To find the length of the hypotenuse, use the Pythagorean Theorem: c = √(a² + b²), where c is the hypotenuse and 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

Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.

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 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 a ladder reaches when placed at a distance from a wall, or finding the shortest distance between two points.

Front

If a ladder is 14 feet long and placed 4 feet from the base of a building, how high does it reach?

Back

Using the Pythagorean Theorem: h = √(14² - 4²) = √(196 - 16) = √180 ≈ 13.4 feet.

Front

What is the formula to find the diagonal of a rectangular solid?

Back

The formula to find the diagonal (d) of a rectangular solid is: d = √(l² + w² + h²), where l is the length, w is the width, and h is the height.

Front

If a rectangular solid has dimensions 3 cm, 4 cm, and 12 cm, what is the length of the diagonal?

Back

Using the formula: d = √(3² + 4² + 12²) = √(9 + 16 + 144) = √169 = 13 cm.

Front

What is the significance of the Pythagorean Theorem in geometry?

Back

The Pythagorean Theorem is fundamental in geometry as it establishes a relationship between the sides of right triangles, allowing for the calculation of unknown side lengths.