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: a² + b² = c².

Tags

CCSS.8.G.B.8

Front

What is the longest side of a right triangle called?

Back

Hypotenuse.

Front

If one leg of a right triangle is 15 and the other leg is 20, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 15² + 20²; c² = 225 + 400; c² = 625; c = 25.

Tags

CCSS.8.G.B.7

Front

How do you find the length of a missing side in a right triangle?

Back

Use the Pythagorean Theorem: a² + b² = c², where a and b are the lengths of the legs and c is the length of the hypotenuse.

Tags

CCSS.8.G.B.7

Front

What is the formula to find the hypotenuse if the legs are known?

Back

c = √(a² + b²).

Tags

CCSS.8.G.B.8

Front

If a right triangle has legs of lengths 6 and 8, what is the length of the hypotenuse?

Back

c = √(6² + 8²) = √(36 + 64) = √100 = 10.

Tags

CCSS.8.G.B.7

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the lengths of the sides satisfy the Pythagorean Theorem: 3² + 4² = 5².

Tags

CCSS.8.G.B.8

Front

What is the value of x in the equation 21² - 15² = x²?

Back

x = √(21² - 15²) = √(441 - 225) = √216 = 14.7.

Tags

CCSS.8.G.B.8

Front

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

Back

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

Tags

CCSS.8.G.B.8

Front

If a ladder is placed 10 feet away from a wall and reaches a height of 24 feet, how long is the ladder?

Back

Using the Pythagorean Theorem: c = √(10² + 24²) = √(100 + 576) = √676 = 26 feet.

Tags

CCSS.8.G.B.8