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a flagpole 25 feet tall stands on a top of a building. from a point in the same horizontal plane with the base of the building. The angle of elevation of the top and the bottom are 61°30' and 56°20' respectively. How high is the building?

  • Trigonometry -

    Draw a picture of the situation:

    1.Draw ver. line AC with A on the bottom.

    2. Add point D on line AC.

    3. Draw a hor. line from A to the left.
    Label it AB. Now we have a rt angle.

    4. Draw hyp. BC.

    5. Draw hyp. BD.

    <ABC = <ABD + <DBC = 61.5o
    56.33 + <DBC = 61.5
    <DBC = 5.17o

    <ACB = 180-(61.5+90) = 28.5o
    <BDC = 180-(28.5+5.17) = 146.33o

    sin5.17/25 = sin146.33/BC
    BC = 153.8 Ft.

    sin61.5 = (25+h)/153.8
    h = 110 Ft. = Ht. of Bldg.

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