Pythagorean Theorem Review

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). This can be expressed as: a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

In the context of the Pythagorean Theorem, what do the variables a, b, and c represent?

Back

In the Pythagorean Theorem, 'a' and 'b' represent the lengths of the two legs of a right triangle, while 'c' represents the length of the hypotenuse.

Front

How can you determine the height of an object using the Pythagorean Theorem?

Back

You can determine the height of an object by creating a right triangle where one leg represents the height, the other leg represents the horizontal distance, and the hypotenuse represents the distance from the object to a point on the ground.

Front

What is the formula to find the length of one leg of a right triangle if the lengths of the other leg and the hypotenuse are known?

Back

If you know the lengths of one leg (a) and the hypotenuse (c), you can find the other leg (b) using the formula: b = √(c² - a²).

Front

What is the relationship between the areas of the squares constructed on the sides of a right triangle?

Back

The sum of the areas of the two smaller squares (on the legs) is equal to the area of the larger square (on the hypotenuse). This is a geometric interpretation of the Pythagorean Theorem.

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 approximate height of a hot air balloon tied to a 200 yd rope, floating 20 yds west of the tie point?

Back

Using the Pythagorean Theorem: height = √(200² - 20²) = √(40000 - 400) = √39600 ≈ 199 yds.

Front

What is the significance of the right angle in a right triangle when using the Pythagorean Theorem?

Back

The right angle is crucial because the Pythagorean Theorem only holds true for right triangles, where one angle measures 90 degrees.

Front

How do you round a number to the nearest tenths place?

Back

To round a number to the nearest tenths place, look at the digit in 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.