Pythagorean Theorem and Distance

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 longest side of a right triangle called?

Back

Hypotenuse.

Front

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

Back

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

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

In a right triangle, if one leg is 6 cm and the hypotenuse is 10 cm, what is the length of the other leg?

Back

8 cm (using the Pythagorean Theorem: 10² = 6² + b²; 100 = 36 + b²; b² = 64; b = 8).

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.

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 ladder is 13 feet long and the foot of the ladder is 5 feet from the wall, how high does it reach on the wall?

Back

12 feet (using the Pythagorean Theorem: 13² = 5² + h²; 169 = 25 + h²; h² = 144; h = 12).

Front

What is the formula to find the area of a right triangle?

Back

Area = (1/2) × base × height.

Front

If a right triangle has legs of lengths 8 cm and 15 cm, what is the length of the hypotenuse?

Back

17 cm (using the Pythagorean Theorem: 8² + 15² = 64 + 225 = 289; √289 = 17).