A 135 ft tower is located on the side of a mountain that is inclined 24° to the horizontal. A guy wire is to be attached to the top of the tower and anchored at a point 40 ft downhill from the base of the tower. Find the shortest length of wire needed. | 135 ft 40 ft 24°

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Problem Description

A 135-foot tower is located on the side of a mountain, inclined at 24° to the horizontal. A guy wire is to be attached to the top of the tower and anchored at a point 40 feet downhill from the base of the tower. The task is to find the shortest length of wire needed.

### Diagram Explanation

- **Slope**: The diagram illustrates a mountain slope inclined at 24°.
- **Tower**: A vertical line represents the 135-foot tower.
- **Guy Wire**: A dashed red line shows the guy wire stretching from the top of the tower to a point on the slope 40 feet from the tower's base.
- **Incline Measurement**: The angle of the slope, 24°, is marked between the horizontal line and the slope.

### Length Calculation

To find the shortest length of the guy wire, apply trigonometry using the inclined plane.

### Additional Information

**NOTE**: The picture is NOT drawn to scale.

**Computation Box**:
- Inputs are required to calculate the length of the guy wire in feet: 
  ```
  length of guy-wire = ______ ft
  ```
Transcribed Image Text:### Problem Description A 135-foot tower is located on the side of a mountain, inclined at 24° to the horizontal. A guy wire is to be attached to the top of the tower and anchored at a point 40 feet downhill from the base of the tower. The task is to find the shortest length of wire needed. ### Diagram Explanation - **Slope**: The diagram illustrates a mountain slope inclined at 24°. - **Tower**: A vertical line represents the 135-foot tower. - **Guy Wire**: A dashed red line shows the guy wire stretching from the top of the tower to a point on the slope 40 feet from the tower's base. - **Incline Measurement**: The angle of the slope, 24°, is marked between the horizontal line and the slope. ### Length Calculation To find the shortest length of the guy wire, apply trigonometry using the inclined plane. ### Additional Information **NOTE**: The picture is NOT drawn to scale. **Computation Box**: - Inputs are required to calculate the length of the guy wire in feet: ``` length of guy-wire = ______ ft ```
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