Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

Help, elevation question?

A woman standing at point A looks up at the top of a building and finds the angle of elevation is 33∘. She walks 407 feet away from the building to point D and finds the angle of elevation to the top of the building is now 25∘. 

What is the height of the building h=___feet?

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  • Philip
    Lv 6
    1 month ago

    Put horizontal distance from base of building = d ft. & building height = h ft.;

    h/d = tan33, ie., h = dtan33...(1).;

    h/(d+407) = tan25, ie., h = (d+407)tan25...(2).;

    By (1) & (2), dtan(33) = (d+407)tan25, ie., d(tan33-tan25)  = 407tan25, ie, d =;

    ((407tan25)/(tan33-tan25)) ft = 1036.522579 ft and (1) now gives h = ;

    1036.522579tan33 ft = 673.1256333 ft = 673 ft rounded off to nearest ft.

  • David
    Lv 7
    1 month ago

    Draw a sketch of two interlinked right angle triangles and by using the 'sine rules' the height of the building works out as 673.1256332 feet or about 673 feet

  • Ian H
    Lv 7
    1 month ago

    h/tan 25 = x + 407

    h/tan 33 = x

    h [1/tan 25 - 1/tan33)] = 407

    h ~ 407/0.6046 ~ 673.1 feet

  • 1 month ago

    Refer to the figure below:

    In the smaller right triangle:

    tan33° = h/x

    x = h/tan33° ...... [1]

    In the larger right triangle:

    tan25° = h/(x + 407)

    x + 407 = h/tan25ᵖ

    x = (h/tan25ᵖ) - 407 …… [2]

    [1] = [2]:

    h/tan33° = (h/tan25ᵖ) - 407

    (h/tan25ᵖ) - (h/tan33°) = 407

    h [(1/tan25ᵖ) - (1/tan33°)] = 407

    h = 407 / [(1/tan25ᵖ) - (1/tan33°)] ft

    h = 673 ft

    The height of the building, h = 673 feet

    Attachment image
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  • ted s
    Lv 7
    1 month ago

    you must be missing something as you state that at 407 from the building the angle is 25° ===> h = 407 tan 25°...want to update the query ?

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