Trig

Two people decide to find the height of an obelisk. They position themselves 25 feet apart in line with, and on the same side of, the obelisk. If they find that the angles of elevation from the ground where they are standing to the top of the obelisk are 65 degrees and 44 degrees, how tall is the obelisk?

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asked by Harry
  1. We draw 2 rt. triangles with a common ver. side:

    1. Draw a hor. line with points A, B, C.
    AB = 25Ft, BC = X Ft.

    2. Draw ver. line CD and label it h.

    3. Draw AD which makes a 44o angle with
    AC.

    Draw BD which forms a 65o angle with BC.

    Tan65 = h/X
    h = X*Tan65 = 2.14X

    Tan44 = h/(25+X)
    h = (25+X)*Tan44
    h = 25.14+0.966X
    Replace h with 2.14X
    2.14x = 25.14+0.966x
    2.14x-0.966x = 25.14
    1.174x = 25.14
    X = 21.4 Ft.

    h = 2.14x = 2.14 * 21.4 = 45.8 Ft.

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    posted by Henry

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