Pythagorean Theorem: Finding Hypotenuse or 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 can be expressed as: c² = a² + b².

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

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), 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 6 inches and the hypotenuse is 10 inches, what is the length of the other leg?

Back

Using the Pythagorean Theorem: b² = c² - a²; b² = 10² - 6²; b² = 100 - 36; b² = 64; b = 8 inches.

Front

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

Back

The formula to calculate the hypotenuse (c) is: c = √(a² + b²).

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, where 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 can you check if a triangle is a right triangle using the Pythagorean Theorem?

Back

To check if a triangle is a right triangle, verify if a² + b² = c² holds true for the lengths of the sides.

Front

What is the approximate length of the other leg if the hypotenuse is 15 inches and one leg is 11 inches?

Back

Using the Pythagorean Theorem: a² = c² - b²; a² = 15² - 11²; a² = 225 - 121; a² = 104; a ≈ 10.2 inches.

Front

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

Back

The Pythagorean Theorem is used in various fields such as architecture, construction, navigation, and physics to calculate distances and design structures.