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 35 degrees and the angle of elevation t

Algebra ->  Customizable Word Problem Solvers  -> Misc -> 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 35 degrees and the angle of elevation t      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1026535: 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 35 degrees
and the angle of elevation to the top of the pole is 7 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?
This is how far i have come up to:

tan(7)=u/x
tan(35)=d/x
u+d=14
Given u = upper part of the pole (35 degrees)
d = lower part of the pole (7 degrees)
I have done all i could but I'm not quite sure if i am right. Surprisingly, i have come up with some unusual values that i am uncertain about, so i just want to compare my answers with yours.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
A little bit of algebra steps:
system%28x%2Atan%287%29=u%2Cx%2Atan%2835%29=d%2Cu%2Bd=14%29

system%28x=u%2Ftan%287%29%2Cx=d%2Ftan%2835%29%2Cu%2Bd=14%29

u=14-d
Substitute.
system%28x=%2814-d%29%2Ftan%287%29%2Cx=d%2Ftan%2835%29%29

Solve either of those for d. Choosing the tan(35) equation,
d=x%2Atan%2835%29, which we already had formed earlier.
Substitute into the tan(7) equation:
x=%2814-%28x%2Atan%2835%29%29%29%2Ftan%287%29

Continue solving for x.
x%2Atan%287%29=14-x%2Atan%2835%29
x%2Atan%287%29%2Bx%2Atan%2835%29=14
x%28tan%287%29%2Btan%2835%29%29=14
highlight%28x=14%2F%28tan%287%29%2Btan%2835%29%29%29-----use either table of values or scientific calculator for computing this.

highlight%28x=10.4%29


--
That was question #1. I did not try question 2.