Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Skills Handbook - The Pythagorean Theorem and the Distance Formula - Exercises: 5

Answer

$$a\approx54.7$$

Work Step by Step

Use the Pythagorean Theorem: $$c^{2}=a^{2}+b^{2}.$$ Rearrange terms: $$a^{2}=c^{2}-b^{2}.$$ Substitute in $b=100$ and $c=114:$ $$a^{2}=114^{2}-100^{2}=12996-10000=2996.$$ Take the square root of both sides and round to the nearest tenth: $$\sqrt {a^{2}}=\sqrt {2996}$$ $$a\approx54.7.$$
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