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 find the length of a missing leg in a right triangle?

Back

To find the length of a missing leg (a or b) in a right triangle, rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a², then take the square root of the result.

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: a² + 5² = 13²; a² + 25 = 169; a² = 144; a = 12.

Front

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

Back

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

Front

In a right triangle, if one leg is 8 and the hypotenuse is 10, what is the length of the other leg?

Back

Using the Pythagorean Theorem: a² + 8² = 10²; a² + 64 = 100; a² = 36; a = 6.

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 a ladder is leaning against a wall and forms a right triangle, how can you find the height it reaches?

Back

Use the Pythagorean Theorem: height² + base² = ladder length². Solve for height.

Front

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

Back

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

Front

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

Back

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

Front

What is the significance of the Pythagorean Theorem in real-life applications?

Back

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to determine distances and angles.