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 is expressed as: a² + b² = c².

Front

What is the formula to find the length of the hypotenuse?

Back

To find the length of the hypotenuse (c) in a right triangle, use the formula: c = √(a² + b²).

Front

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

Back

The length of the hypotenuse is 5, 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

If the lengths of the two legs of a right triangle are 5 and 12, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 13, calculated as: c = √(5² + 12²) = √(25 + 144) = √169 = 13.

Front

What does 'a' and 'b' represent in the Pythagorean Theorem?

Back

'a' and 'b' represent the lengths of the two legs (the sides that form the right angle) of a right triangle.

Front

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

Back

The length of the other leg is 8, calculated as: b = √(10² - 6²) = √(100 - 36) = √64 = 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 right triangle has legs of lengths 8 and 15, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 17, calculated as: c = √(8² + 15²) = √(64 + 225) = √289 = 17.