Pythagorean Theorem (Simplest Radical Form)

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

What does 'simplest radical form' mean?

Back

Simplest radical form refers to a square root that has been simplified so that there are no perfect square factors left under the radical sign.

Front

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

Back

Using the Pythagorean Theorem: c² = 3² + 4² = 9 + 16 = 25. Therefore, c = √25 = 5.

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. Rearrange the formula based on which side is missing: a² = c² - b² or b² = c² - a².

Front

What is the hypotenuse in a right triangle?

Back

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

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

If the hypotenuse is 10 and one side is 6, what is the length of the other side?

Back

Using the Pythagorean Theorem: a² = c² - b². Here, a² = 10² - 6² = 100 - 36 = 64. Therefore, a = √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. The shortest side is opposite the 30-degree angle.

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

How do you simplify √50?

Back

√50 can be simplified to 5√2 because 50 = 25 * 2, and √25 = 5.