Pythagorean Theorem

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 formula to find the length of the hypotenuse?

Back

The formula to find the length of the hypotenuse (c) in a right triangle is: c = √(a² + b²).

Front

If one side of a right triangle is 3 and the other side is 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

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 side opposite the 30° angle is the shortest.

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 length of the hypotenuse is √2 times the length of each leg.

Front

How do you estimate the square root of a number?

Back

To estimate the square root of a number, find two perfect squares between which the number lies and then approximate based on their square roots.

Front

What is the square root of 16?

Back

The square root of 16 is 4, since 4 x 4 = 16.

Front

If the hypotenuse of a right triangle is 10 and one side is 6, how do you find the other side?

Back

Use the Pythagorean Theorem: a² + 6² = 10². Therefore, a² + 36 = 100, so a² = 64, and a = 8.

Front

What is the value of y if a right triangle has sides of length 5 and y, and a hypotenuse of 13?

Back

Using the Pythagorean Theorem: 5² + y² = 13². Therefore, 25 + y² = 169, so y² = 144, and y = 12.

Front

What is the importance of the Pythagorean Theorem in real life?

Back

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