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From a point B that is 9 meters above level ground , the angle of elevation of the top of a building is 43 degrees and the angle of depression of the base of the building is 7 degrees. What is the height of the building.

(tell what formula and why you used it will very much be appreciated)

  • precal -

    draw a horizontal line from B to where it intersects the building wall. Call that point C.

    Label the top of the building A, and the bottom D.

    The height of the building is thus

    AD = AC + CD

    AC/BC = tan 43°
    CD/BC = tan 7°

    Now, you see that without knowing the distance BC, there is no way to determine the height of the building. The farther away you are, the higher the building.

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