Suppose you are standing next to a tall building and wish to know the building's height. A light post
that is 20 feet tall casts a shadow that is 14 feet long. The shadow from the building is measured to be
100 feet. Determine the height of the building.

x = 142.85, or the Height of the Building is 142.85

Step-by-step explanation:

If I am right this is a proportion.

Building:

Height - X

Shadow - 100ft

Light Pole:

Height - 20ft

Shadow - 14ft

Basically these 2 are equal to each-other. So we use proportional math. Height over shadow, and then we butterfly multiply. So!

 =    

To multiply and find the answer we butterfly multiply, 20x100 = 2000,

and then 14x(x) = 14x so we have 2000 = 14x. We have to solve for X, so we divide both sides by 14 to get X alone.

2000/14 = 142.85 and 14x/14 = x. In the end, we have x = 142.85.

Hope this helps!

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: