To estimate the height of a building, two students find the angle of elevation from a point (at ground level) down the street from the building to the top of the building is 40°. From a point that is 250 feet closer to the building, the angle of elevation (at ground level) to the top of the building is 57°. If we assume that the street is level, use this information to estimate the height of the building.

here is a big fat

step-by-step explanation:

given that ab is divided into equal parts as

ac, cd, de, ef, fg, gh, hi, ib.

from this we find that f is the midpoint of ab.

so using mid point formula we find

f = (3,7)

similarly considering fb, we get

h = mid point of fb = ((6,6) and g, mid point of fh is

g = (9/2, 13/2)

i is mid point of hb

so i =(15/2,11/2)

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: