How do you use the pythagorean theorem to find the missing side given c = 19, b = 4a; find a and b?

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Answer 1 · 2017-01-18T19:51:50

$a = 4.608$ rounded to the nearest thousandth.

and

$b = 18.433$ rounded to the nearest thousandth.

The Pythagorean theorem states:

$a^2 + b^2 = c^2$

Where $a$ and $b$ are the lengths of the sides of a right triangle and $c$ is the length of the hypotenuse of the right triangle.

Susbtituting $color(red)(19)$ for $c$ and $color(blue)(4a)$ for $b$ we can solve for $a$ :

$a^2 + (color(blue)(4a))^2 = color(red)(19)^2$

#a^2 + 16a^2 = 361

$17a^2 = 361$

$(17a^2)/color(red)(17) = 361/color(red)(17)$

#(color(red)(cancel(color(black)(17)))a^2)/cancel(color(red)(17)) = 21.235

$a^2 = 21.235$ rounded to the nearest thousandth.

$sqrt(a^2) = sqrt(21.235)$

$a = 4.608$ rounded to the nearest thousandth.

Then we can solve for $b$ by substituting $4.608$ for $a$ in the relationship: $b = 4a$

$b = 4 xx 4.608$

$b = 18.433$ rounded to the nearest thousandth.