Question

Question #f2f9f

Answer 1

See a solution process below:

Explanation:

We can use the Pythagorean Theorem to solve this problem.

The Pythagorean Theorem states, for a right triangle:

`a^2 + b^2 = c^2`

Where `a` and `b` are sides of the triangle. And, `c` is the hypotenuse of the right triangle or the side opposite the right triangle.

Assuming the flagpole is at a right angle to the ground, then the wire would be the side opposite the right triangle or in other words the hypotenuse. So, `c` would be 35 feet.

The flagpole and the distance the stake is from the base of the flagpole would be the two sides of the right triangle.

Therefore we could make `a` equal to 14 feet and would could solve for `b`.

Substituting and solving for `b` gives:

`(14"ft")^2 + b^2 = (35"ft")^2`

`196"ft"^2 + b^2 = 1225"ft"^2`

`196"ft"^2 - color(red)(196"ft"^2) + b^2 = 1225"ft"^2 - color(red)(196"ft"^2)2`

`0 + b^2 = 1029"ft"^2`

`b^2 = 1029"ft"^2`

`sqrt(b^2) = sqrt(1029"ft"^2)`

`b = sqrt(1029"ft"^2)`

`b = sqrt(49 * 21"ft"^2)`

`b = sqrt(49)sqrt(21)sqrt("ft"^2)`

`b = 7sqrt(21)sqrt"ft"`

Or, if a number is required:

`b = 32"ft"` rounded to the nearest whole foot.

The height of the flag pole would be approximately 32 feet tall.