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Math Help - Word problem angle of elevation/depression. HELP!

  1. #1
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    Word problem angle of elevation/depression. HELP!

    Please help. I have no idea how to get this.

    From the top of the building, the angle of elevation of the top of a 120 ft tower is 10 degrees. From a window 6ft below the top of the building, the angle of depression of the base of the tower is 30 degrees. Determine the height of the building and the distance between the tower and the building.

    Please help. Please include an illustration of the problem. Thanks
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by reiward View Post
    Please help. I have no idea how to get this.

    From the top of the building, the angle of elevation of the top of a 120 ft tower is 10 degrees. From a window 6ft below the top of the building, the angle of depression of the base of the tower is 30 degrees. Determine the height of the building and the distance between the tower and the building.

    Please help. Please include an illustration of the problem. Thanks
    in the picture I attached

    Y+X+6=120....(1)

    \tan 10^0=\frac{X}{D}....(2)

    \tan 30^0=\frac{Y}{D}.....(3)

    find X ,Y with respect to D
    From (2)
    D\tan 10^0 = X

    From (3)
    D\tan 30^0= Y

    sub X,Y values in (1)

    D\tan 10^0+D\tan 30^0+6 =120

    Word problem angle of elevation/depression. HELP!-mod.jpg

    Edited: Fix the error
    Last edited by Amer; August 11th 2009 at 07:41 AM.
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by Amer View Post
    in the picture that I attached you can see that

    x+120=6+y=\text{the building height}

    \tan 10^0 = \frac{x}{D} .....(1)

    \tan 30^0 = \frac{y}{D}.......(2)

    find D value with respect to x,y
    from (1)

    x=D\tan 10^0

    from (2)
    y=D\tan 30^0 sub D values in x+120=6+y


    D\tan 30^0 + 120 = D\tan 10^0 + 6 equation with one variable you can find it
    Attachment 12456
    Amer,

    I read it as though the tower was taller than the building and the angle of elevation from the top of the building to the top of the tower is 10 degrees. Your figure shows the angle of depression to the top of the tower is 10 degrees.
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  4. #4
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by masters View Post
    Amer,

    I read it as though the tower was taller than the building and the angle of elevation from the top of the building to the top of the tower is 10 degrees. Your figure shows the angle of depression to the top of the tower is 10 degrees.
    Thanks Master

    I forgot to see the meaning of elevation in the dictionary sorry I fixed the error
    Last edited by Amer; August 11th 2009 at 07:34 AM.
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  5. #5
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    Quote Originally Posted by Amer View Post
    in the picture I attached

    Y+X+6=120....(1)

    \tan 10^0=\frac{X}{D}....(2)

    \tan 30^0=\frac{Y}{D}.....(3)

    find X ,Y with respect to D
    From (2)
    D\tan 10^0 = X

    From (3)
    D\tan 30^0= Y

    sub X,Y values in (1)

    D\tan 10^0+D\tan 30^0+6 =120

    Click image for larger version. 

Name:	Mod.JPG 
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ID:	12457

    Edited: Fix the error
    thank you so much!
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