Pythagorean Triples & Special Right Triangles

Front

What is a Pythagorean Triple?

Back

A set of three positive integers a, b, and c that satisfy the equation a² + b² = c².

Front

List the first three Pythagorean Triples.

Back

(3, 4, 5), (5, 12, 13), (8, 15, 17).

Front

What is the formula to find the hypotenuse in a right triangle?

Back

c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.

Front

If one leg of a right triangle is 6 and the other leg is 8, what is the length of the hypotenuse?

Back

10 (using the Pythagorean theorem: √(6² + 8²) = √(36 + 64) = √100 = 10).

Front

What is a special right triangle?

Back

A triangle with specific angle measures that allow for easy calculation of side lengths, such as 45-45-90 and 30-60-90 triangles.

Front

In a 45-45-90 triangle, if the legs are of length x, what is the length of the hypotenuse?

Back

x√2.

Front

In a 30-60-90 triangle, if the shortest side is x, what are the lengths of the other sides?

Back

The lengths are x (shortest side), x√3 (longer leg), and 2x (hypotenuse).

Front

Determine if the following set of numbers are Pythagorean Triples: 5, 12, 13.

Back

Yes, because 5² + 12² = 25 + 144 = 169 = 13².

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

The ratio of the lengths of the sides is 1 : √3 : 2.

Front

If 36 and 48 are the two smaller numbers in a Pythagorean Triple, what is the third number?

Back

60 (since 36² + 48² = 1296 + 2304 = 3600 = 60²).