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The Pont du Gard near Nimes, France is a roman aqueduct. An observer in a hot air balloon some distance away from the aqueduct determines that the angle of depression to each end is 54 degrees and 71 degrees respectively the horizontal distance between the balloon and aqueduct is 270.0 m. Calculate the length of the aqueduct to the nearest thenth of a metre.

  • Math -

    Nada, can you send me the answer so I
    can compare with mine before posting?

  • Math -

    To help you understand what I've done,
    we'll draw a picture of the problem:

    1. Draw a rectangle with the longest
    sides in hor. positiion and the shortest sides vertically.

    2. Draw a diagonal from the upper
    left vertex to the lower right vertex.

    3. Draw a 2nd line from the upper left
    vertex to a point near the center of
    the bottom line. Label the portion to
    the lt. 270 m and the portion to the rt. X meters.

    4. Label the angle between the top
    line of the rectangle and the diag-
    onal 54 deg. This is the angle of
    depression.

    5. At the lower right vertex, the diag.
    forms 2 angles. Label the one on the left 54 deg. also. We have formed 2 rt. triangles. The angle between the
    top line of the rectangle and the shortest hyp. is the 2nd angle
    of depression and measures 71 deg.

    6. Label the acute angle formed by the smaller hyp. and the bottom of the
    rectangle 71 deg.

    Tan 71 = h / 270, h = 270 Tan 71 =
    784.14 m. = Height of observer.
    Tan 54 = 784.14 / (X = 270),
    (X + 270) Tan 54 = 784.14
    X + 270 = 784.14 / Tan 54 = 569.7
    X = 569.7 - 270 = 299.7 m = Length of
    Aqueduct

  • Math -

    Thanks so much !

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