Question

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

Answer 1

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:

`(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