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

Mar 20, 2018

See a solution process below:

Explanation:

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

The Pythagorean Theorem states:

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:

${\left(21 \text{ft")^2 + b^2 = (35"ft}\right)}^{2}$

$441 {\text{ft"^2 + b^2 = 1225"ft}}^{2}$

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

$0 + {b}^{2} = 784 {\text{ft}}^{2}$

${b}^{2} = 784 {\text{ft}}^{2}$

$\sqrt{{b}^{2}} = \sqrt{784 {\text{ft}}^{2}}$

$b = 28 \text{ft}$

The measure of the other leg is 28 feet