Pythagorean Theorem

Front

What does the Pythagorean Theorem state?

Back

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). This can be expressed as: c² = a² + b².

Front

What is the formula to find the hypotenuse in a right triangle?

Back

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

Front

If side a = 8 and side b = 5, what is the length of side c?

Back

Using the Pythagorean Theorem: c = √(8² + 5²) = √(64 + 25) = √89 ≈ 9.4.

Front

What is the term used for the longest side of a right triangle?

Back

The longest side of a right triangle is called the hypotenuse.

Front

How do you find a missing side of a right triangle if you know the hypotenuse and one other side?

Back

You can rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a², then take the square root to find the missing side.

Front

What is the value of side c if a = 6 and b = 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.

Front

What is the value of x if c = 34.8 and b = 30?

Back

Using the Pythagorean Theorem: x = √(c² - b²) = √(34.8² - 30²) = √(1213) ≈ 34.8.

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, engineering, and physics to calculate distances and design structures.

Front

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

Back

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