Lesson6homeworkpracticeusethepythagoreantheoremanswerkey

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How to Use the Pythagorean Theorem to Solve Problems: Lesson 6 Homework Practice Answer Key

The Pythagorean theorem is a mathematical formula that relates the lengths of the sides of a right triangle. It states that the square of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the other two sides. The formula can be written as:

c = a + b

where c is the hypotenuse, and a and b are the other two sides.

The Pythagorean theorem can be used to find the missing length of any side of a right triangle, as long as you know the lengths of the other two sides. You can also use it to check if a triangle is right or not, by plugging in the lengths of the sides and seeing if the equation holds true.

In this article, we will show you how to use the Pythagorean theorem to solve some common problems that you might encounter in your homework or in real life. We will also provide you with an answer key for lesson 6 homework practice, where you can check your answers and see how to work out each problem step by step.

Problem 1: Finding the Hypotenuse

One of the most basic applications of the Pythagorean theorem is finding the length of the hypotenuse of a right triangle, given the lengths of the other two sides. For example, suppose you have a right triangle with sides of 3 cm and 4 cm. How long is the hypotenuse

To solve this problem, you need to plug in the values of a and b into the Pythagorean theorem, and then solve for c. Here are the steps:

Write down the formula: c = a + b

Substitute the values of a and b: c = 3 + 4

Simplify: c = 9 + 16

Add: c = 25

Take the square root of both sides: c = â25

Simplify: c = 5

The answer is 5 cm. The hypotenuse of the right triangle is 5 cm long.

Problem 2: Finding a Missing Side

You can also use the Pythagorean theorem to find the length of one of the shorter sides of a right triangle, given the lengths of the hypotenuse and the other side. For example, suppose you have a right triangle with a hypotenuse of 13 cm and one side of 5 cm. How long is the other side

To solve this problem, you need to plug in the values of c and one of a or b into the Pythagorean theorem, and then solve for the other one. Here are the steps:

Write down the formula: c = a + b

Substitute the values of c and one of a or b: 13 = 5 + b

Simplify: 169 = 25 + b

Subtract 25 from both sides: b = 144

Take the square root of both sides: b = â144

Simplify: b = 12

The answer is 12 cm. The other side aa16f39245