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 find the length of one side of a right triangle using the Pythagorean Theorem?

Back

To find the length of one side, rearrange the Pythagorean Theorem formula. For example, to find side a: a = √(c² - b²).

Front

If a ladder reaches a height of 12 feet and is placed 15 feet away from the wall, how do you find the length of the ladder?

Back

Use the Pythagorean Theorem: c = √(12² + 15²) = √(144 + 225) = √369 ≈ 19.2 feet.

Front

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

Back

The distance can be calculated using the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

In a right triangle, if one leg is 3 units and the other leg is 4 units, what is the length of the hypotenuse?

Back

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

Front

How do you solve a word problem involving the Pythagorean Theorem?

Back

Identify the right triangle, assign variables to the sides, apply the Pythagorean Theorem, and solve for the unknown side.

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, where 1 is the length of the side opposite the 30-degree angle.

Front

If a soccer field is 90 meters wide and 120 meters long, how do you find the diagonal distance?

Back

Use the Pythagorean Theorem: d = √(90² + 120²) = √(8100 + 14400) = √22500 = 150 meters.

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle, and is crucial for applying the Pythagorean Theorem.

Front

How can you determine if a triangle is a right triangle?

Back

Use the Pythagorean Theorem: if a² + b² = c² holds true for the sides, then the triangle is a right triangle.