Two vertical poles PQ and ST are secured by a rope PRS going from the top of the first pole to a point R on the ground between the poles and then to the top of the second pole as in the figure. If R is chosen to minimize the length of the rop Find the ratio 01 02 in terms of a and b where a is the length of PQ andb is the length of ST. R

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

Two vertical poles, PQ and ST, are secured by a rope PRS. The rope extends from the top of the first pole, P, to a point, R, on the ground between the poles, and then to the top of the second pole, S, as depicted in the figure. If R is chosen to minimize the length of the rope, find the ratio \(\frac{\theta_1}{\theta_2}\) in terms of \(a\) and \(b\), where \(a\) is the length of PQ and \(b\) is the length of ST.

### Diagram Explanation

The diagram displays two vertical poles, PQ and ST, with the ground extending between points Q and T. The rope forms angles \(\theta_1\) and \(\theta_2\) with the horizontal at points P and S respectively. These angles are shown at the point where rope segments PR and RS contact the ground at R. The segment PR is inclined from P to R, and segment RS from R to S.

### Solution Task

- **Objective**: Find the ratio of the angles \(\frac{\theta_1}{\theta_2}\).
- **Parameters**:
  - \(a\): Length of pole PQ.
  - \(b\): Length of pole ST.

Base your calculations and reasoning using these parameters.
Transcribed Image Text:### Problem Description Two vertical poles, PQ and ST, are secured by a rope PRS. The rope extends from the top of the first pole, P, to a point, R, on the ground between the poles, and then to the top of the second pole, S, as depicted in the figure. If R is chosen to minimize the length of the rope, find the ratio \(\frac{\theta_1}{\theta_2}\) in terms of \(a\) and \(b\), where \(a\) is the length of PQ and \(b\) is the length of ST. ### Diagram Explanation The diagram displays two vertical poles, PQ and ST, with the ground extending between points Q and T. The rope forms angles \(\theta_1\) and \(\theta_2\) with the horizontal at points P and S respectively. These angles are shown at the point where rope segments PR and RS contact the ground at R. The segment PR is inclined from P to R, and segment RS from R to S. ### Solution Task - **Objective**: Find the ratio of the angles \(\frac{\theta_1}{\theta_2}\). - **Parameters**: - \(a\): Length of pole PQ. - \(b\): Length of pole ST. Base your calculations and reasoning using these parameters.
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