If a=5 and c=9, how do you find b?

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If a=5 and c=9, how do you find b?

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Answer 1 · 2015-10-08T19:33:30

Assuming you are speaking of the lengths of the sides of a right-angled triangle:

$b = \sqrt{c^{2} - a^{2}} = \sqrt{81 - 25} = \sqrt{56} = 2 \sqrt{14}$ $b = sqrt(c^2-a^2) = sqrt(81-25) = sqrt(56) = 2 sqrt(14)$

Explanation:

Pythagoras theorem tells us: $a^{2} + b^{2} = c^{2}$ $a^2 + b^2 = c^2$

Subtract $a^{2}$ $a^2$ from both sides to get:

$b^{2} = c^{2} - a^{2}$ $b^2 = c^2 - a^2$

Then take the (positive) square root of both sides to get:

$b = \sqrt{c^{2} - a^{2}}$ $b = sqrt(c^2 - a^2)$

In our case, $a = 5$ $a = 5$ and $c = 9$ $c = 9$ , so...

$b = \sqrt{9^{2} - 5^{2}} = \sqrt{81 - 25} = \sqrt{56}$ $b = sqrt(9^2 - 5^2) = sqrt(81 - 25) = sqrt(56)$

$= \sqrt{2^{2} \cdot 14} = \sqrt{2^{2}} \cdot \sqrt{14} = 2 \sqrt{14}$ $= sqrt(2^2 * 14) = sqrt(2^2)*sqrt(14) = 2 sqrt(14)$

$\approx 7.4833$ $~~ 7.4833$

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If a=5 and c=9, how do you find b?

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