Pythagorean Theorem Word Problems Practice

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: a² + b² = c².

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 the length of side 'a', use: a = √(c² - b²).

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

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

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° angle, the longer leg is opposite the 60° angle, and the hypotenuse is the longest 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 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 12 inches and a height of 16 inches?

Back

Using the Pythagorean Theorem: d = √(12² + 16²) = √(144 + 256) = √400 = 20 inches.

Front

In a word problem, how do you identify the right triangle?

Back

Look for a scenario involving perpendicular lines or a situation where you can visualize a right angle, such as a ladder leaning against a wall or a ramp.

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).

Front

If a ladder is 20 feet long and the base is 15 feet from the wall, how high does it reach?

Back

Using the Pythagorean Theorem: height = √(20² - 15²) = √(400 - 225) = √175 ≈ 13.2 feet.