**Problem Statement:**A belt is to go around two pulleys of radii 1 inch and 2 inches with centers 6 inches apart. How long should the belt be? **Hint:** To find the length of the upper half of the belt begin by computing: (i) The distance \( d \) with similar triangles. (ii) The length \( h \) using an argument involving similar triangles and the Pythagorean Theorem. (iii) The angles \(\theta\), \(\alpha\), and \(\beta\) using right triangle trigonometry.---**Diagram Explanation:**The diagram illustrates two circles representing the pulleys with different radii. The smaller pulley on the left has a radius of 1 inch, and the larger pulley on the right has a radius of 2 inches. The centers of the pulleys are 6 inches apart.- The x-axis is aligned horizontally between the centers of the two pulleys.- A triangle is formed by: - A horizontal line segment \( h \) between the points on the circumferences. - A vertical segment from the center of the smaller pulley to the horizontal segment, indicated by \( y \). - A sloped segment forming the hypotenuse of the triangle.- The angles \(\theta\), \(\alpha\), and \(\beta\) are marked at various junctions in the diagram, showing their positions relative to the belt’s path and pulley centers.Through this geometric setup, the problem guides calculating the required dimensions and angles using similar triangles, trigonometry, and the Pythagorean Theorem.

Answered: Image /qna-images/answer/37c3b700-22a8-4747-8702-106dfa02a56e.jpg

Answered: 2. A belt is to go around two pulleys…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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