Finding the Hypotenuse of a Right Triangle

Front

What is the hypotenuse of a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

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 3 feet and the other leg is 4 feet, what is the length of the hypotenuse?

Back

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

Front

How do you find the length of the hypotenuse if you know the lengths of the two legs?

Back

Use the Pythagorean theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the lengths of the legs.

Front

What is the relationship between the legs and the hypotenuse in a right triangle?

Back

The hypotenuse is always longer than either leg in a right triangle.

Front

If the hypotenuse is 10 feet and one leg is 6 feet, how do you find the other leg?

Back

Use the Pythagorean theorem: b = √(c² - a²) = √(10² - 6²) = √(100 - 36) = √64 = 8 feet.

Front

What is the formula to calculate the distance between two points in a coordinate plane?

Back

The distance formula is d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

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

Back

12 feet (using the Pythagorean theorem: b = √(c² - a²) = √(13² - 5²) = √(169 - 25) = √144 = 12).

Front

What is the significance of the right angle in a right triangle?

Back

The right angle (90 degrees) is crucial because it allows the use of the Pythagorean theorem to find the lengths of the sides.

Front

How can you determine if a triangle is a right triangle?

Back

If the lengths of the sides satisfy the Pythagorean theorem (a² + b² = c²), then it is a right triangle.