How do you use the Pythagorean Theorem to find the missing side of the right triangle with the given measures: A= 8, C= 16?

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Answer 1 · 2018-04-12T13:27:41

The missing side of the right triangle is #sqrt192#

The formula for the Pythagorean Theorem is #a^2 + b^2 = c^2#

You are given a=8 and c=16 so plug those numbers into the formula:

#8^2 + b^2 = 16^2#

#64 + b^2 = 256#

Subtract 64 from both sides

#b^2 = 192#

Square root both sides to get rid of the exponent

#sqrt(b^2) = sqrt192#

#b = sqrt192#

#----------#

To simplify #sqrt192# :

Factor 64 out of 192

#sqrt(64(3))#

Rewrite 64 as #8^2#

#sqrt(8^2 * 3)#

Pull terms out from under the radical

#8sqrt3#

The result can be shown in both exact and decimal forms.

Exact Form:
#8sqrt3#

Decimal Form:
13.856406456 . . .