A guy wire is a cable used to restrain objects from moving. They are used to support towers or poles. A guy wire is attached to a cell tower. The 45-foot long guy wire is attached to a tower such that the angle formed by the ground and the wire measures 32°. The guy wire is replaced by a guy wire 100 feet long. The point at which the new guy wire attaches to the tower is the same as it was with the original wire. What is the approximate measure of the angle formed by this new guy wire and the ground?

The new angle is ( θn ) = 13.2°  

Step-by-step explanation:

Solution:-

- Draw a right angle triangle, using a guy wire of length L = 45 ft, draw the hypotenuse between two legs.

- Denote the height "h" from which the wire is attached to the tower and denote base "b" as the distance from the foot of the tower and pole.

- The angle between the guy wire with length L = 45 ft and the ground is θ = 32°.

- Use appropriate trigonometric ratio relation to determine the height "h" at which the guy is attached to support tower:

                       sin ( θ ) = h / L  

                       h = L*sin ( θ )

                       h = 45*sin ( 32 )

                       h =23.84636 ft

- Another guy wire of length Ln = 100 ft is used instead of previous guy wire of length L = 45 ft. The height "h" at which the guy is attached to support tower is to be kept constant.

- Again, using the appropriate trigonometric ratio relation to determine the new angle ( θn ) between the wire and ground:

                      sin ( θn ) = h / Ln

                      sin ( θn ) = 23.84636 / 100

                     ( θn ) = arc sin [ 0.23846]

                    ( θn ) = 13.2°  

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step-by-step explanation: