Pythagorean Theorem - Solving for Legs

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

How do you solve for a missing leg in a right triangle using the Pythagorean Theorem?

Back

To solve for a missing leg (a or b), rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a². Then take the square root to find the length.

Front

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

Back

Using the Pythagorean Theorem: c² = a² + b², we have 13² = 5² + b². This simplifies to 169 = 25 + b², so b² = 144, and b = 12.

Front

What is the length of the hypotenuse if both legs are 6?

Back

Using the Pythagorean Theorem: c² = 6² + 6² = 36 + 36 = 72. Therefore, c = √72 = 6√2 or approximately 8.49.

Front

If a right triangle has legs of lengths 8 and 15, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 8² + 15² = 64 + 225 = 289. Therefore, c = √289 = 17.

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

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

Back

Using the Pythagorean Theorem: c² = a² + b², we have 10² = 6² + b². This simplifies to 100 = 36 + b², so b² = 64, and b = 8.

Front

What is the formula to find 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

If a right triangle has legs of lengths 9 and 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 9² + 12² = 81 + 144 = 225. Therefore, c = √225 = 15.

Front

What is the length of the missing side if one leg is 7 and the hypotenuse is 25?

Back

Using the Pythagorean Theorem: c² = a² + b², we have 25² = 7² + b². This simplifies to 625 = 49 + b², so b² = 576, and b = 24.