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: a² + b² = c².

Front

How do you identify a right triangle?

Back

A right triangle is identified by having one angle that measures exactly 90 degrees.

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

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

Back

Using the Pythagorean Theorem: 3² + 4² = c²; 9 + 16 = c²; 25 = c²; c = 5 units.

Front

What is the formula to find the length of a missing side in a right triangle?

Back

To find a missing side, rearrange the Pythagorean Theorem: c² = a² + b² or a² = c² - b² or b² = c² - a².

Front

In a ladder problem, if the ladder is 25 feet long and placed 10 feet away from the wall, how high does it reach?

Back

Using the Pythagorean Theorem: 10² + h² = 25²; 100 + h² = 625; h² = 525; h = √525 ≈ 22.9 feet.

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

If a flagpole is 26 feet tall and a string is attached 18 feet away from the base, how long is the string?

Back

Using the Pythagorean Theorem: 18² + 26² = s²; 324 + 676 = s²; s² = 1000; s ≈ 31.6 feet.

Front

How can you find the distance across a pond if you walk 34 meters south and 41 meters east?

Back

Use the Pythagorean Theorem: 34² + 41² = d²; 1156 + 1681 = d²; d² = 2837; d ≈ 53 meters.

Front

What is a real-world application of the Pythagorean Theorem?

Back

The Pythagorean Theorem can be used in construction to determine the correct length of ladders, ramps, or to ensure structures are level.