Pythagorean Theorem (finding leg)

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

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

Back

To find the length of a missing leg (a) in a right triangle, rearrange the Pythagorean Theorem: a = √(c² - b²) if b is known, or b = √(c² - a²) if a is known.

Front

If one leg of a right triangle is 10 and the hypotenuse is 12, what is the length of the other leg?

Back

Using the Pythagorean Theorem: a² + 10² = 12². Therefore, a² + 100 = 144, so a² = 44, and a = √44 ≈ 6.6.

Front

What is the hypotenuse of a right triangle with legs of lengths 6 and 8?

Back

Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10.

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° angle, the longer leg is opposite the 60° angle, and the hypotenuse is twice the shortest side.

Front

What is the height of a right triangle if the base is 12 and the hypotenuse is 15?

Back

Using the Pythagorean Theorem: h = √(15² - 12²) = √(225 - 144) = √81 = 9.

Front

What does it mean for a triangle to be a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees. The side opposite this angle is called the hypotenuse.

Front

If a right triangle has legs of lengths 5 and 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(5² + 12²) = √(25 + 144) = √169 = 13.

Front

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

Back

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

Front

In a right triangle, if one leg is 9 and the hypotenuse is 15, what is the length of the other leg?

Back

Using the Pythagorean Theorem: b = √(15² - 9²) = √(225 - 81) = √144 = 12.