SOLUTION: A sign is erected over top a street by attaching a wire to two lamp posts on either side of the street. If the wire hangs down 3.5 m from the point of attachment on the lamp posts

Question 1204917: A sign is erected over top a street by attaching a wire to two lamp posts on either side of the street. If the wire hangs down 3.5 m from the point of attachment on the lamp posts and the sign hangs 1.7 m closer to the lamp on the right. Find the angles of depression of the wire.
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Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Diagram

The horizontal segments DF and FC add to 32.0 meters since AB = 32.0

DF + FC = 32.0
x + x - 1.7 = 32.0
2x - 1.7 = 32.0
2x = 32.0 + 1.7
2x = 33.7
x = 33.7/2
x = 16.85

For right triangle DEF we have legs DF = x = 16.85 and EF = 3.5
tan(angle) = opposite/adajcent
tan(D) = EF/DF
tan(D) = 16.85/3.5
tan(D) = 4.814286
D = arctan(4.814286)
D = 78.265663
Angle FDE = 78.265663 is one approximate angle of depression on the left side.

Now focus on right triangle CEF.
FC = x - 1.7 = 16.85 - 1.7 = 15.15
then,
tan(angle) = opposite/adajcent
tan(C) = EF/FC
tan(C) = 3.5/15.15
tan(C) = 0.231023
C = arctan(0.231023)
C = 13.008421
Angle FCE = 13.008421 is another approximate angle of depression on the right side.

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