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 are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle. They are usually referred to as 'a' and 'b' in the Pythagorean Theorem.

Front

If one leg of a right triangle is 5 cm and the other leg is 12 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 5² + 12² = 25 + 144 = 169. Therefore, c = √169 = 13 cm.

Front

What is the length of the missing side if the hypotenuse is 10 cm and one leg is 6 cm?

Back

Using the Pythagorean Theorem: 10² = 6² + b². Thus, 100 = 36 + b², so b² = 64, and b = √64 = 8 cm.

Front

In a right triangle, if the hypotenuse is 15 cm and one leg is 9 cm, what is the length of the other leg?

Back

Using the Pythagorean Theorem: 15² = 9² + b². Thus, 225 = 81 + b², so b² = 144, and b = √144 = 12 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 shortest side is opposite the 30° angle, the longer leg is opposite the 60° angle, and the hypotenuse is the longest 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 right triangle has legs of lengths 8 cm and 15 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 8² + 15² = 64 + 225 = 289. Therefore, c = √289 = 17 cm.

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

If a right triangle has a hypotenuse of 25 cm and one leg of 20 cm, what is the length of the other leg?

Back

Using the Pythagorean Theorem: 25² = 20² + b². Thus, 625 = 400 + b², so b² = 225, and b = √225 = 15 cm.