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)#

Pythagoras theorem tells us: #a^2 + b^2 = c^2#

Subtract #a^2# from both sides to get:

#b^2 = c^2 - a^2#

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

#b = sqrt(c^2 - a^2)#

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

#b = sqrt(9^2 - 5^2) = sqrt(81 - 25) = sqrt(56)#

#= sqrt(2^2 * 14) = sqrt(2^2)*sqrt(14) = 2 sqrt(14)#

#~~ 7.4833#