SOLUTION: A woman standing on the top of a hill sees a flagpole that she knows is 14 meter tall. The angle of depression to the bottom of the pole is 7 degrees and the angle of elevation to

Question 1025720: A woman standing on the top of a hill sees a flagpole that she knows is 14 meter tall. The angle of depression to the bottom of the pole is 7 degrees and the angle of elevation to the top of the pole is 35 degrees.
1. Find her distance from the flag pole.
2. Given that the flag pole is placed on the same ground level as the hill and the woman is 1.73 meter tall. How high is the hill?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your diagram looks like this as far as i can tell.

$$$

from this diagram, you get:

tan(35) = x/y

tan(7) = (14-x)/y

solve for y to get:

y = x/tan(35) and y = (14-x)/tan(7)

this results in x/tan(35) = (14-x)/tan(7)

multiply both sides of this equation by tan(7) * tan(35) to get:

x*tan(7) = (14-x)*tan(35)

simplify to get:

x*tan(7) = 14*tan(35) - x*tan(35)

add x*tan(35) to both sides of this equation to get:

x*tan(7) + x*tan(35) = 14*tan(35)

factor out the x to get:

x*(tan(7) + tan(35)) = 14*tan(35)

divide both sides of this equation by (tan(7) + tan(35)) to get:

x = (14*tan(35)) / (tan(7) + tan(35)

solve for x to get:

x = 11.91129969

14-x is therefore equal to 14 - 11.91129969 = 2.08870031

y = x/tan(35) results in y = 11.91129969/tan(35) which results in y = 17.01109891

y = (14-x)/tan(7) results in y = 2.08870031/tan(7) which results in y = 17.01109891.

value of y looks good either way.

looking at the diagram, we see that:

BC = x = 11.91129969

CD = 14 - x = 2.08870031

BD = the height of the flagpole = BC + CD = 14.

y = AC = the distance between the woman and the flagpole = 17.01109891.

AE = distance between the height of the woman and the ground = 14 - x = 2.08870031.

since the height of the woman is 1.73, then the hill she is standing on must be 2.08870031 - 1.73 = .3587003101.

looks like we have everything you need.

her distance to the flagpole is 17.01109891 meters.

the height of the hill is .3587003101 meters.

i double checked my results and i believe they are correct.

hopefully you agree after looking at what i did.

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