If the garage is 18 ft. wide and the owner wants the arch to have a height of 12
ID: 3427412 • Letter: I
Question
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? 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 hori tal line of garage to center of circle radius of circle r Center of Circle 18 feet Write a system of two equations with two unknowns (r and y) and solve the system of equations using substitution or elimination.Explanation / Answer
12 inch = 1ft
r = y + 1
rsin(theta) = 9 => r2sin2(theta) = 81 .....(1)
rcos(theta) = y = r -1 => r2cos2(theta) = r2 - 2r + 1 ....(2)
adding (1) and (2)
r2 = r2 - 2r + 1 + 81
2r = 82
r = 41 feet
y = 40 ft