Pythagorean Theorem Word Problems

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.

Tags

CCSS.8.G.B.8

Front

How do you find the length of the diagonal of a rectangle?

Back

To find the length of the diagonal (d) of a rectangle, use the Pythagorean Theorem: d = √(width² + height²).

Tags

CCSS.8.G.B.7

Front

If a right triangle has legs of lengths 3 feet and 4 feet, what is the length of the hypotenuse?

Back

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

Tags

CCSS.8.G.B.7

Front

In a right triangle, if one leg is 6 feet and the hypotenuse is 10 feet, how long is the other leg?

Back

Using the Pythagorean Theorem: b = √(10² - 6²) = √(100 - 36) = √64 = 8 feet.

Tags

CCSS.8.G.B.7

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 opposite the 90° angle.

Tags

CCSS.HSG.CO.C.10

Front

How do you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle is a right triangle, check if the square of the longest side equals the sum of the squares of the other two sides. If a² + b² = c², then it is a right triangle.

Tags

CCSS.8.G.B.8

Front

What is the height of a ladder leaning against a wall if the ladder is 25 feet long and the base is 20 feet from the wall?

Back

Using the Pythagorean Theorem: height = √(25² - 20²) = √(625 - 400) = √225 = 15 feet.

Tags

CCSS.8.G.B.8

Front

If a ramp has a vertical height of 4 feet and a horizontal length of 3 feet, what is the length of the ramp?

Back

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

Tags

CCSS.8.G.B.8

Front

What is the formula for the distance between two points in a coordinate plane?

Back

The distance (d) between two points (x1, y1) and (x2, y2) is given by the formula: d = √((x2 - x1)² + (y2 - y1)²).

Tags

CCSS.HSG.GPE.B.7

Front

How far is a point 8 feet above the ground and 6 feet horizontally from the base of a wall?

Back

Using the Pythagorean Theorem: distance = √(8² + 6²) = √(64 + 36) = √100 = 10 feet.

Tags

CCSS.8.G.B.8