Answer: 9 inches.
Do the pythagorean theorem to find your answer.
Formula: a^2 + b^2 = c2
12 = b
15 = c
a^2 + 12^2 = 15^2
Simplify the equation
a^2 + 144 = 225
Subtract 144 on both sides.
a^2 = 81
Square root of 81 is 9.
In your question where as ask to find which angel of rotation will image of the polygon coincide with the pre-image if a 12 sided regular polygon rotates about its center. I think the angle is 30 degrees because the polygon has total of 360 degree then divide it to 12 then you will came up with a 30
I'm not sure if that's the correct method of finding that (it could be, I was just never shown that kind of method). What I did was multiply everything out, that way you have two numbers vs two equations. Then add those two numbers and turn that into scientific notation.