A person is remodeling the front entrance to his home and needs to cut an arch for the top of an entranceway. The arch needs to be $36 ft$ wide and $6 ft$ high. To draw the arch, he will use a stretched string with chalk attached at an end as a compass.
a) Using a coordinate system, locate the center of the circle
b) What radius should the person use to draw the arch?
a) The center of the circle is $(0, - 24)$ .
(Type an ordered pair.)
b) To draw the arch, the person should use a radius of [ (Type an integer or a fraction.)
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Answer

$r = \frac{\sqrt{1296 + 36}}{2}$

Steps

Step 1 ： $(x - 0)^{2} + (y + 24)^{2} = r^{2}$

Step 2 ： $r^{2} = 36^{2} + 6^{2}$

Step 3 ： $r = \frac{\sqrt{1296 + 36}}{2}$