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 type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

In the Pythagorean Theorem, what do the variables a, b, and c represent?

Back

In the Pythagorean Theorem, 'a' and 'b' represent the lengths of the two legs of the right triangle, while 'c' represents the length of the hypotenuse.

Front

How do you find the length of the hypotenuse using the Pythagorean Theorem?

Back

To find the length of the hypotenuse, use the formula c = √(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

Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5 feet.

Front

What is the distance from the top of a 10-foot ladder leaning against a wall, if the bottom is 4 feet away from the wall?

Back

Using the Pythagorean Theorem: c = √(10² - 4²) = √(100 - 16) = √84 ≈ 9.17 feet.

Front

What is the formula to find the length of a missing side in a right triangle?

Back

The formula is a² + b² = c², where you can rearrange it to find a or b if c is known.

Front

If the hypotenuse of a right triangle is 13 and one leg is 5, how do you find the other leg?

Back

Use the formula: b = √(c² - a²). Here, b = √(13² - 5²) = √(169 - 25) = √144 = 12.

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.