## Algebra 2 Common Core

Published by Prentice Hall

# Skills Handbook - The Pythagorean Theorem and the Distance Formula - Exercises - Page 981: 6

#### Answer

$$b\approx 27.6$$

#### Work Step by Step

Use the Pythagorean Theorem: $$c^{2}=a^{2}+b^{2}.$$ Rearrange terms: $$b^{2}=c^{2}-a^{2}.$$ Substitute in $a=12.0$ and $c=30.1:$ $$b^{2}=(30.1)^{2}-(12.0)^{2}=906.01-144.00=762.01.$$ Take the square root of both sides and round to the nearest tenth: $$\sqrt {b^{2}}=\sqrt {762.01}$$ $$b\approx 27.6.$$

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