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 the hypotenuse in a right triangle?

Back

To find the length of the hypotenuse, use the Pythagorean Theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the lengths of the other two sides.

Front

If one side of a right triangle is 6 units and the other side is 8 units, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10 units.

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 in a coordinate plane, such as finding the shortest path between two locations.

Front

In a right triangle, if the lengths of the two legs are equal, what type of triangle is it?

Back

It is an isosceles right triangle, where the angles opposite the equal sides are both 45 degrees.

Front

How can the Pythagorean Theorem be used in construction?

Back

In construction, the Pythagorean Theorem is used to ensure that structures are built at right angles, helping to create accurate and stable designs.

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 the shortest side is opposite the 30-degree angle.

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 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

If a ladder is placed 10 feet away from a wall and reaches a height of 25 feet, how long is the ladder?

Back

Using the Pythagorean Theorem: c = √(10² + 25²) = √(100 + 625) = √725 ≈ 26.93 feet.