anonymous
  • anonymous
What is the length of AC?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
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anonymous
  • anonymous
|dw:1332371597643:dw|
anonymous
  • anonymous
Time to bust out the Pythagorean Theorem. You remember that one, yes? \[a ^{2}+b ^{2}=c ^{2}\] What you also want to recall about it is: \[(leg)^{2}+(leg)^{2}=(hypotenuse)^{2}\] The legs are the sides coming out of the 90 degree angle, so yours look to be 5 and 15. Honestly, it doesn't matter which is a and which is b. \[(5)^{2}+(15)^{2}=c ^{2}\] Now, you're doing order of operations: First take care of those exponents. \[25+225=c ^{2}\] Then add the two numbers on the left together \[250=c ^{2}\] Then take the square root of both sides \[\sqrt{250}=\sqrt{c ^{2}}\] So, finally: \[c=\sqrt{250}\] Now, depending on what your teacher wants, you can simplify this a bit. Start by making a factor tree for 250. |dw:1332372146783:dw| From here, we can rewrite: \[\sqrt{250}=\sqrt{2\times5\times5\times5}=5\sqrt{2\times5}=5\sqrt{10}\] Now, mathematically, we would want to consider a positive answer and a negative answer, but because we're talking about a distance, the negative answer is tossed out. :)

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