Step-By-Step-Math: Using the Pythagorean Theorem to Find a Missing Leg Length of a Right Triangle
Find the Missing Leg Length of a Right Triangle | Pythagorean Theorem Step by Step
Learning Target: I can use the Pythagorean theorem to find a missing leg length of a right triangle
What You'll Learn
- Identify the hypotenuse and legs of a right triangle
- Determine whether the missing side is a leg or the hypotenuse
- Set up the Pythagorean theorem equation
- Solve for a missing side length
Key Terms
right triangle, hypotenuse, leg, Pythagorean theorem, square root
Standards Alignment
- CCSS.MATH.CONTENT.8.G.B.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles
- CCSS.MATH.CONTENT.8.G.B.8: Apply the Pythagorean Theorem to find the distance between two points
Math Practices
- MP1: Make sense of problems and persevere in solving them
- MP2: Reason abstractly and quantitatively
- MP6: Attend to precision
Chapters
- 0:00 How do you find a missing side of a right triangle?
- 0:14 What is the Pythagorean theorem?
- 0:26 What is a hypotenuse?
- 0:38 What are the legs of a right triangle?
- 0:48 How do you decide if the missing side is a leg or the hypotenuse?
- 1:02 How do you label the sides a, b, and c?
- 1:14 How do you substitute into the Pythagorean theorem?
- 1:24 How do you square each number?
- 1:34 How do you isolate the unknown?
- 1:46 Why do we subtract and not add?
- 1:58 How do you solve for the missing side?
- 2:10 How do you check your answer?
▶ Click to Read Full Transcript
[00:00] Let's find the missing leg length of a right triangle step by step. We are given a right triangle where one leg length is 6, the second leg length is unknown, and the hypotenuse length is 10. Our instructions are to find the missing side.
[00:15] The tool we need is the Pythagorean theorem. The Pythagorean theorem says that in a right triangle, a squared plus b squared equals c squared.
[00:25] But wait! Before we use the formula, we need to understand what a, b, and c mean. The letter c is always the hypotenuse. The hypotenuse is the longest side of a right triangle, and it is always the side across from the right angle. It is always the longest side.
[00:45] The letters a and b are the two legs. The legs are the two shorter sides that form the right angle. It does not matter which leg you call a and which you call b.
[00:57] Let's label everything. One leg, a, equals 6. The other leg, b, is what we are solving for. The hypotenuse, c, equals 10.
[01:10] Now substitute our values into the Pythagorean theorem. Wherever we see a, we write 6. Wherever we see c, we write 10. We leave b as b because that is what we are solving for. We get 6 squared plus b squared equals 10 squared.
[01:29] Next, square the numbers we know. 6 squared means 6 times 6, which is 36. And 10 squared means 10 times 10, which is 100. So we have 36 plus b squared equals 100.
[01:45] Now we need to get b squared by itself. To do that, subtract 36 from both sides. On the left side, 36 minus 36 cancels out, leaving just b squared. On the right side, 100 minus 36 is 64.
[02:04] To solve for b, take the square root of both sides. The square root undoes the squaring. The square root of 64 is plus or minus, 8, because 8 times 8 equals 64, and negative 8 times negative 8 also equals 64. Our triangle is a right triangle with positive side lengths, so b equals positive 8.
[02:26] Let's check our answer. If the three sides are 6, 8, and 10, then 6 squared plus 8 squared should equal 10 squared. 36 plus 64 is 100, and 10 squared is 100. It checks out.
[02:43] The missing leg length is 8.
[02:46] I hope you found this helpful along your journey to discovering the joy in mathematics. This has been Mister Marx AI. Until next time, keep up the good work!
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