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Math Help - Angle of Elevation Help

  1. #1
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    Angle of Elevation Help

    From a point 200 feet from a flagpole, the angles of elevation to the bottom and top of the flagpole are 16.75 degrees and 18 degrees, respectively. Find the height of the flagpole to the nearest foot.

    I have a hard time drawing a picture for this. I think there's two triangles involved, but I'm not sure where the numbers go.
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  2. #2
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    Quote Originally Posted by College Student View Post
    From a point 200 feet from a flagpole, the angles of elevation to the bottom and top of the flagpole are 16.75 degrees and 18 degrees, respectively. Find the height of the flagpole to the nearest foot.
    The pole must be on some sort of hill or platform, for the bottom of the pole to be elevated above the observer's ground level.

    Draw a horizontal line for the ground level. Draw slanty lines for the two line-of-sight lines. Draw a vertical line for the pole, extending this line down to the horizontal line.

    The horizontal, vertical, and slanty lines form two nested right triangles. The vertical line is split into two pieces: the height of the pole and the remaining distance from the base of the pole to the horizontal line. Label the top part as "h" and the other part as, say, "x".

    The shared horizontal base can be labelled as "200".

    Label the two angles, and then use the trig ratios related to x/200 and (x + h)/200 to create two equations in x and h. Use these to solve for the value of h.

    If you get stuck, please reply showing how far you have gotten. Thank you!
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