From the window in an apartment building, the angle of elevation to the top of a flag pole across the street is 9 degrees. The angle of depression to the base of the flag pole is 22 degrees. We are also given the height of the building which is 8 meters.

Question

I would like to know how to do this problem so I would like to the steps required thank you for all your help! I have the question as a link but am not allowed to post URL's.

Answer 1

I forgot the say that I am trying to determine the height of the flagpole to the nearest tenth of a metre!

Answer 2

I assume that the window is at a height of 8 meters, not the building.
Draw a diagram, and draw a horizontal line from the window to the pole. Now you can place some labels.
W = window in building
T = top of pole
P = point on pole even with the window
B = bottom of pole
Now what do you know?
BP = 8
PB/PW = tan22°, so PW = 8/tan22° = 19.8
PT/PW = tan9°, so PT = 19.8 tan9° = 3.136
The pole's height is BP+PT = 22.9 m

Answer 3

Thank you so much!

Answer 4

Make your sketch.
Label the top of the pole as P and its bottom as Q
I drew a horizontal from his window to meet the flagpole at A
let PA = x

I will assume you meant the height of the window of the building to be 8 m
then AQ = 8
You now have two right-angled triangle. Let his position at the window be B
from the top triangle: tan 9°= x/AB
AB = x/tan9°
from the bottom triangle: tan22° = 8/AB
AB = 8/tan22

so x/tan9 = 8/tan22
x = 8tan9/tan22 = .... , add this to 8 to get the flagpole height.

Let me know if I did not interpret your question correctly.

Answer 5

I believe oobleck added PW to 3.136
instead of 8 + 3.136

Answer 6

Reiny is correct. I added the distance between the building and the pole, rather than the 8m below the window.