A construction company frequently builds garages with an arch over the garage, similar to the one in the figure below. In order to build the arch, they need to consider the entire circle, thus where the center of the circle is and the radius of the circle. Currently, they guess and check until they get the correct height of the arch. For your information, a construction management student at BYU-Idaho brought this question to a mathematics faculty member for assistance in solving. a. If the garage is 18 ft. wide and the owner wants the arch to have a height of 12 in., what is the radius of the circle that is necessary to cut the arch? b. This question can be answered through building and solving a system of nonlinear equations. It may be hard to consider a system of equations without a grid behind the picture and some labels. So, to assist you in this question, a more detailed picture is provided. 12 inches 9 feet y= distance from horipontal line of garage to cente of circle radiusof circle =r Center of Circle 18 feet c. Write a system of two equations with two unknowns (r and y) and solve the system of equations using substitution or elimination.

A construction company frequently builds garages with an arch over the garage, similar to the one in the figure below. In order to build the arch, they need to consider the entire circle, thus where the center of the circle is and the radius of the circle. Currently, they guess and check until they get the correct height of the arch. For your information, a construction management student at BYU-Idaho brought this question to a mathematics faculty member for assistance in solving. a. If the garage is 18 ft. wide and the owner wants the arch to have a height of 12 in., what is the radius of the circle that is necessary to cut the arch? b. This question can be answered through building and solving a system of nonlinear equations. It may be hard to consider a system of equations without a grid behind the picture and some labels. So, to assist you in this question, a more detailed picture is provided. 12 inches 9 feet y= distance from horipontal line of garage to cente of circle radiusof circle =r Center of Circle 18 feet c. Write a system of two equations with two unknowns (r and y) and solve the system of equations using substitution or elimination.

Elementary Geometry for College Students

6th Edition

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Daniel C. Alexander, Geralyn M. Koeberlein

Chapter6: Circles

Section6.3: Line And Segment Relationships In The Circle

Problem 38E: The center of a circle of radius 3 inches is at a distance of 20 inches from the center of a circle...

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