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

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 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 cm and the other side is 4 cm, what is the length of the hypotenuse?

Back

5 cm (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √25 = 5).

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), you can treat the difference in x and y as the two sides of a right triangle. The distance (d) is given by: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the formula to calculate the area of a right triangle?

Back

The area (A) of a right triangle can be calculated using the formula: A = (1/2) * base * height.

Front

In a right triangle, if one side is 8 cm and the hypotenuse is 10 cm, what is the length of the other side?

Back

6 cm (using the Pythagorean Theorem: 10² = 8² + b², so 100 = 64 + b², thus b² = 36, and b = 6).

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.

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

If a ladder is placed 12 feet away from a wall and reaches a height of 16 feet, how long is the ladder?

Back

20 feet (using the Pythagorean Theorem: 12² + 16² = 144 + 256 = 400, so the ladder length is √400 = 20).