If a triangle has a leg of 21 ft, and a hypotenuse of 35 ft, what is the measure of the other leg?

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Answer 1 · 2018-03-20T13:09:23

See a solution process below:

Note: Assumption is this is a right or $90^o$ triangle.

For a right triangle

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

Where:

$a$ and $b$ are legs of the right triangle and $c$ is the hypotenuse.

Substituting for $a$ and $c$ and solving for $b$ gives:

$(21"ft")^2 + b^2 = (35"ft")^2$

$441"ft"^2 + b^2 = 1225"ft"^2$

$441"ft"^2 - color(red)(441"ft"^2) + b^2 = 1225"ft"^2 - color(red)(441"ft"^2)$

$0 + b^2 = 784"ft"^2$

$b^2 = 784"ft"^2$

$sqrt(b^2) = sqrt(784"ft"^2)$

$b = 28"ft"$

The measure of the other leg is 28 feet