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A communications tower is located at the top of a steep hill, as shown. The angle of inclination of the hill is 62°. A guy wire is to be attached to the top of the tower and to the ground, 163 ft downhill from the base of the tower. The angle formed by the guy wire is 10°. Find the length of the cable required for the guy wire.

A communications tower is located at the top of a steep hill, as shown. The angle of inclination of the hill is 62°. A guy wire is to be attached to the top of the tower and to the ground, 163 ft downhill from the base of the tower. The angle formed by the guy wire is 10°. Find the length of the cable required for the guy wire.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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A communications tower is located at the top of a steep hill, as shown. The angle of inclination of the hill is 62°. A guy wire is to be attached to the top of the tower and to the ground, 163 ft downhill from the base of the tower. The angle formed by the guy wire is 10°. Find the length of the cable required for the guy wire.

### Description of the Diagram The diagram illustrates a scenario involving a communications tower located at the top of a hill. Key elements include measurements and angles relevant to finding the length of a guy wire that stabilizes the tower. #### Diagram Details: 1. **Location of the Tower:** - The tower is situated at the peak of a sloped hill, indicated by red lines. 2. **Guy Wire:** - Represented by a dashed red line running from the top of the tower to the base. - The angle that the guy wire makes with the horizontal at the point of attachment is marked as \(10^\circ\). 3. **Base Angles:** - The angle at the base of the slope (where it meets the horizontal ground) is \(62^\circ\). 4. **Horizontal Distance:** - The horizontal distance from the base of the tower to the point where the slope meets the ground is labeled as \(163\) feet. ### Explanation for Educational Purpose This type of problem typically involves solving for the length of the guy wire using trigonometric principles. By understanding the angles involved and the given horizontal distance, one can employ trigonometric functions like sine, cosine, or tangent to calculate the total length of the guy wire. The information provided is crucial for applying the Law of Sines or Law of Cosines, depending on the available data points and required solutions.
Transcribed Image Text:### Description of the Diagram The diagram illustrates a scenario involving a communications tower located at the top of a hill. Key elements include measurements and angles relevant to finding the length of a guy wire that stabilizes the tower. #### Diagram Details: 1. **Location of the Tower:** - The tower is situated at the peak of a sloped hill, indicated by red lines. 2. **Guy Wire:** - Represented by a dashed red line running from the top of the tower to the base. - The angle that the guy wire makes with the horizontal at the point of attachment is marked as \(10^\circ\). 3. **Base Angles:** - The angle at the base of the slope (where it meets the horizontal ground) is \(62^\circ\). 4. **Horizontal Distance:** - The horizontal distance from the base of the tower to the point where the slope meets the ground is labeled as \(163\) feet. ### Explanation for Educational Purpose This type of problem typically involves solving for the length of the guy wire using trigonometric principles. By understanding the angles involved and the given horizontal distance, one can employ trigonometric functions like sine, cosine, or tangent to calculate the total length of the guy wire. The information provided is crucial for applying the Law of Sines or Law of Cosines, depending on the available data points and required solutions.
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