Pythagorean Theorem Word Problems Flashcard 1

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

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

If one leg of a right triangle 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

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

Back

The distance formula is: d = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

How do you round a number to the nearest tenth?

Back

To round a number to the nearest tenth, look at the hundredths place. If it is 5 or greater, round up the tenths place by one. If it is less than 5, keep the tenths place the same.

Front

What is the diagonal length of a rectangle with a width of 6 units and a height of 8 units?

Back

Using the Pythagorean Theorem: d = √(6² + 8²) = √(36 + 64) = √100 = 10 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 shortest side is opposite the 30-degree angle, the longer leg is opposite the 60-degree angle, and the hypotenuse is opposite the right angle.

Front

If a square has a side length of 5 units, what is the length of its diagonal?

Back

Using the Pythagorean Theorem: d = √(5² + 5²) = √(25 + 25) = √50 ≈ 7.07 units.

Front

What is the significance of the Pythagorean Theorem in real-life applications?

Back

The Pythagorean Theorem is used in various real-life applications such as construction, navigation, and physics to determine distances and relationships between different points.