Beth has 2000 feet of fencing available to enclose a rectangular field. one side of the field lies along a river, so only three sides require fencing. express the area a of the rectangle as a function of x, where x is the length of the side parallel to the river.

 

Step-by-step explanation:

Perimeter (P) is the total length of the fencing which covers 2 sides of one length and 1 side of another length (because the side along the river does not need fencing).  So, P = 2L+ x  where L is the length and x is the width.

P = 2000 and P = 2L + x   →   2000 = 2L + x

Area (A) is length x width  →  A = L × x

So for this question we need to make a triangle.
So:
|\
| \23
|_\
7
Imagine the hypotenuse is the ladder (23ft) and the straight line is the wall, so the base is the space between the ladder and the wall (7ft).
So to find the angle of elevation it would be the angle in the bottom right, as that is the angle that the ladder is slanted at. As this is a right angle triangle you can use SOH CAH TOA
So we have h (23) and a(7) so we can do inverse cos 7/23 to get 72.28 degrees which rounds to 72.3.

Then to find the height on the building we can use Pythagoras’ theorem:
A^2 + b^2 = c^2 where c is the hypotenuse.
So we know c= 23 and b= 7
So we rearrange to get
C^2 - b^2 = a^2
So
529 - 49 = 480 which is a^2 so we square root that to get 21.9 which rounds to 22 feet.