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.
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.
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
I believe oobleck added PW to 3.136
instead of 8 + 3.136
I forgot the say that I am trying to determine the height of the flagpole to the nearest tenth of a metre!
Thank you so much!
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.
Reiny is correct. I added the distance between the building and the pole, rather than the 8m below the window.
No problem! I can guide you through the steps to solve this problem.
Step 1: Draw a diagram
Start by drawing a diagram to visualize the given information. Draw a building represented as a vertical line, a flagpole represented by another vertical line across the street, and a window on the building. Label the angles and the length of the building's height.
Step 2: Identify the trigonometric functions
In this problem, we are given the angle of elevation (9 degrees) and the angle of depression (22 degrees). We need to use trigonometry to find the height of the flagpole. To do this, we will use the tangent function for the angle of elevation and the angle of depression.
Step 3: Calculate the height of the flagpole
To calculate the height of the flagpole, use the following formula:
Height of flagpole = (Height of building + Distance from window to flagpole) * tan(angle of elevation)
In this case, the distance from the window to the flagpole is not provided. However, this distance is not necessary for this problem, as we can eliminate it while solving.
Step 4: Substitute the given values into the formula
Substitute the given values into the formula:
Height of flagpole = (8 + Distance from window to flagpole) * tan(9 degrees)
Step 5: Solve for Distance from window to flagpole
To solve for the distance from the window to the flagpole, rearrange the formula:
Distance from window to flagpole = Height of flagpole / tan(9 degrees) - 8 meters
Step 6: Substitute the values and calculate
Substitute the height of the flagpole and the angle of elevation into the equation:
Distance from window to the flagpole = (Height of flagpole / tan(9 degrees)) - 8 meters
By substituting the known values into the equation, you will be able to calculate the distance from the window to the flagpole.
Remember to always double-check your calculations and use a calculator if necessary.