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.

Front

How do you identify the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

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

Back

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

Front

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

Back

The Pythagorean Theorem can be used to determine the distance between two points, such as finding the length of a ladder needed to reach a certain height when placed a certain distance from the wall.

Front

In the context of word problems, what does 'distance apart' usually refer to?

Back

'Distance apart' refers to the straight-line distance between two points, which can often be calculated using the Pythagorean Theorem.

Front

What is the formula to find the length of a diagonal in a rectangle?

Back

The length of the diagonal (d) can be found using the formula: d = √(length² + width²).

Front

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

Back

Using the Pythagorean Theorem: c² = 26² + 18²; c² = 676 + 324; c² = 1000; c = √1000 ≈ 31.6 feet.

Front

How do you set up a Pythagorean Theorem problem from a word problem?

Back

Identify the two legs of the right triangle from the problem, assign them as 'a' and 'b', and the hypotenuse as 'c'. Then use the formula c² = a² + b².

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 are in a ratio that satisfies the Pythagorean Theorem: 3² + 4² = 5².

Front

If a slide is 6 feet tall and the base is 8 feet, how long is the slide?

Back

Using the Pythagorean Theorem: c² = 6² + 8²; c² = 36 + 64; c² = 100; c = 10 feet.