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 distance between two points using the Pythagorean Theorem?

Back

To find the distance between two points (x1, y1) and (x2, y2) on a coordinate plane, use the formula: Distance = √((x2 - x1)² + (y2 - y1)²). This is derived from the Pythagorean Theorem.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees. The side opposite the right angle is called the hypotenuse.

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: c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5 units.

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 side opposite the 30° angle is the shortest, the side opposite the 60° angle is √3 times the shortest side, and the hypotenuse is twice the shortest side.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

How do you apply the Pythagorean Theorem to real-world problems?

Back

To apply the Pythagorean Theorem to real-world problems, identify the right triangle formed by the situation, label the sides, and use the theorem to find the unknown side.

Front

What is the formula for the diagonal of a rectangle?

Back

The formula for the diagonal (d) of a rectangle with width (w) and height (h) is: d = √(w² + h²).

Front

If a rectangular field is 50 yards wide and 100 yards long, how far is it across the diagonal?

Back

Using the formula: d = √(50² + 100²); d = √(2500 + 10000); d = √12500; d ≈ 111.80 yards.