Pythagorean Theorem Applications

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 is expressed as a² + b² = c².

Front

What is the formula to find the length of the hypotenuse in a right triangle?

Back

The formula to find the length of the hypotenuse (c) in a right triangle is c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

How do you calculate the length of a side in a right triangle if the hypotenuse and one side are known?

Back

If the hypotenuse (c) and one side (a) are known, the length of the other side (b) can be calculated using the formula b = √(c² - a²).

Front

What is the length of the hypotenuse if the other two sides are 4 and 5?

Back

Using the Pythagorean Theorem: c = √(4² + 5²) = √(16 + 25) = √41.

Front

If the hypotenuse is 10 and one side is 6, what is the length of the other side?

Back

Using the formula b = √(c² - a²): b = √(10² - 6²) = √(100 - 36) = √64 = 8.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem only applies to right triangles.

Front

What is a right triangle?

Back

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

Front

How can you determine if three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths.

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle and is opposite the right angle.