Pythagorean Theorem

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, commonly referred to as sides a and b.

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

If one leg of a right triangle is 30 and the other leg is 40, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 50 (using the Pythagorean Theorem: 30² + 40² = c², so 900 + 1600 = c², thus c = 50).

Front

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

Back

To find the length of a missing side, use the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse and a and b are the legs.

Front

What is the length of the hypotenuse if the legs are 24 and 7?

Back

The length of the hypotenuse is approximately 25 (using the Pythagorean Theorem: 24² + 7² = c², so 576 + 49 = c², thus c ≈ 25).

Front

In a right triangle, if one leg is 8 and the hypotenuse is 10, what is the length of the other leg?

Back

The length of the other leg is 6 (using the Pythagorean Theorem: 10² = 8² + b², so 100 = 64 + b², thus b = 6).

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the sum of the squares of the lengths of the two legs equals the square of the length of the hypotenuse.

Front

If a ladder is placed 10 feet away from a wall and reaches a height of 24 feet, how long is the ladder?

Back

The length of the ladder is 26 feet (using the Pythagorean Theorem: 10² + 24² = c², so 100 + 576 = c², thus c = 26).

Front

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

Back

The area of a right triangle can be calculated using the formula: Area = (1/2) * base * height.

Front

If the hypotenuse of a right triangle is 13 and one leg is 5, what is the length of the other leg?

Back

The length of the other leg is 12 (using the Pythagorean Theorem: 13² = 5² + b², so 169 = 25 + b², thus b = 12).