# Math

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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.

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can compare with mine before posting?

• Math -

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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