Calculating Side Lengths with the Pythagorean Theorem
To find the length of the hypotenuse (c), add the squares of the legs and take the square root: c = \sqrt{a^2 + b^2} To find the length of a leg (e.g., a), subtract the square of the other leg from the square of the hypotenuse and take the square root: a = \sqrt{c^2 - b^2}. The calculation method depends on which side of the right triangle is unknown. To find the hypotenuse (the longest side), you must add the squares of the two legs before taking the square root. This skill is part of Grade 8 math in enVision, Mathematics, Grade 8.
Key Concepts
To find the length of the hypotenuse ($c$), add the squares of the legs and take the square root: $$c = \sqrt{a^2 + b^2}$$ To find the length of a leg (e.g., $a$), subtract the square of the other leg from the square of the hypotenuse and take the square root: $$a = \sqrt{c^2 b^2}$$.
Common Questions
What is Calculating Side Lengths with the Pythagorean Theorem?
To find the length of the hypotenuse (c), add the squares of the legs and take the square root: c = \sqrt{a^2 + b^2} To find the length of a leg (e.g., a), subtract the square of the other leg from the square of the hypotenuse and take the square root: a = \sqrt{c^2 - b^2}.
How does Calculating Side Lengths with the Pythagorean Theorem work?
Example: Finding the hypotenuse: A right triangle has legs of length a = 9 and b = 12. Find the hypotenuse c. c = \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15
Give an example of Calculating Side Lengths with the Pythagorean Theorem.
Finding a leg: A right triangle has a hypotenuse of length c = 13 and one leg of length b = 5. Find the other leg a. a = \sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12
Why is Calculating Side Lengths with the Pythagorean Theorem important in math?
The calculation method depends on which side of the right triangle is unknown. To find the hypotenuse (the longest side), you must add the squares of the two legs before taking the square root.
What grade level covers Calculating Side Lengths with the Pythagorean Theorem?
Calculating Side Lengths with the Pythagorean Theorem is a Grade 8 math topic covered in enVision, Mathematics, Grade 8 in Chapter 7: Understand and Apply the Pythagorean Theorem. Students at this level study the concept as part of their grade-level standards and are expected to explain, analyze, and apply what they have learned.
How does Calculating Side Lengths with the Pythagorean Theorem connect to other math topics?
To find the hypotenuse (the longest side), you must add the squares of the two legs before taking the square root. To find a leg (one of the two shorter sides), you must subtract the square of the known leg from the square of the hypotenuse, then take the square root. Be careful not to mix up addition and subtraction, and always remember the final square root step to find the side's length..