A woman standing on a hill sees a flagpole that she knows to be 60 ft tall. the angle of depression to the bottom of the pole is 14 degrees and the angle of elevation to the top of the pole is 18 degrees. find her horizontal distance to the flagpole.
Let H=horizontal distance to the pole
Vertical distance
=Htan(θ)
where θ is the angle of depression.
Thus
60' = Htan(θ2)-Htan(θ1)
=H(tan(18°)-tan(14°))
Solve for H to get
H = 60'/(tan(18°)-tan(14°))
=?
To find the horizontal distance to the flagpole, we can use trigonometric functions.
Let's assume that the woman is standing at point A, the base of the flagpole is at point B, and the top of the flagpole is at point C. We need to find the distance from point A to point B, which we'll call x.
First, let's calculate the vertical distance (h) from point A to point C, which is the height of the flagpole:
h = height of flagpole = 60 ft
Next, let's calculate the vertical distance (y) from point A to point B, by using the angle of depression:
y = h * tan(angle of depression)
y = 60 ft * tan(14 degrees)
Now, let's calculate the horizontal distance (x) from point A to point B using the angle of elevation:
x = y + h * tan(angle of elevation)
Substituting the values we already know:
x = y + 60 ft * tan(18 degrees)
Now, we can substitute the value of y and calculate the value of x:
x = (60 ft * tan(14 degrees)) + (60 ft * tan(18 degrees))
Calculating this expression will give you the horizontal distance (x) from the woman to the flagpole.