Question 9616
This is a right triangle problem so we can use the Pythagorean Theorem that says: {{{A^2+B^2=C^2}}}

We know the ladder is 17 Ft. Tall and leaning against the wall and the bottom of the ladder is 7 Ft out from the wall.

So we will make the height of the wall where the top of the ladder is = A

The distance (7 Ft.) from the wall out to the bottom of the ladder = B

and the length of the ladder (17 Ft.) = C

So A & B are legs on the right Triangle and C is the hypotenuse of the Triangle.

Now we can solve the problem.

We now put the numbers in for the variables we know and the equation looks like this:  {{{A^2+7^2=17^2}}}

Now we solve the equation, lets isolate A^2 by subtracting 7^2 from both sides:
{{{A^2+7^2-7^2=17^2-7^2}}} so this becomes {{{A^2=17^2-7^2}}}

Now lets sqaure our numbers so: {{{A^2=289-49}}} or {{{A^2=240}}}

Now lets lets get rid of the square on the A by taking the square root of both sides so: {{{sqrt(A^2)=sqrt(240)}}} = {{{A=15.49}}}

Now we know the ladder is 15.49 Ft. up the side of the building.

Lets check it with our formula {{{A^2+B^2=C^2}}}

{{{15.49^2+7^2=17^2}}} = {{{239.94+49=289}}} = {{{288.94=289}}} We will round up to 289.  Close enough for goverment work.