# Thread: Can you help me find some angles and distances in a rectangle *pic inside*

1. ## Can you help me find some angles and distances in a rectangle *pic inside*

I am basically trying to find "x" and "y" the 2.5" line is perpendicular to the center point. Drawing an imaginary circle between the cuts.

Been trying to use the Pythagorean theorem but i guess I am a little rusty can anyone explain how to solve?

Can we assume that the dashed lines meet in the center of the rectangle and would, if extended past those perpendiculars go through the corners of the rectangle? If so, what I would do is set up a coordinate system with origin at the center, x-axis parallel to the 27" sides and y-axis parallel to the 13.5" sides. The top of the rectangle is y= 13.5/2= 6.75 and the right side of the rectangle is x= 27/2= 13.5. The line from the center to the top right corner is y= (6.75/13.5)x= x/2 so has slope 1/2. A line perpendicular to that has slope -2 so can be written y= -2x+ C for some constant, C. The point at which that line crosses the top of the rectangle is y= -2x+ C= 6.75 so (x, 7)= (C- 6.75)/2, 6.75) and the point at which that line crosses the right of the rectangle is (x, y)= (13.5, -27+ C) The d-istance between those two points is $\displaystyle \sqrt{(13.5- (C- 6.75))^2+ (6.75- (-27+ C))^2}= \sqrt{(20.25- C)^2+ (33.75- C)^2}= 2.5$. Solve that for C. The two distance you want are A=13.5- (C- 6.75)= 20.257 and B= 6.75- (-27+ C)= 33.75- C.