Given a point A at (X,Y) which is inside the rectangle defined by the points (9,9), (9,78), (150,9), and (150, 78), and also given an angle θ which represents the direction in which point A will begin moving (θ=0 representing the positive x direction), I'm trying to find the distance r point A will travel before hitting one of the rectangle's sides. Here's the code I threw together initially to solve the problem:

Repeat X+Rcos(θ)≥150 or X+Rcos(θ)≤9 or Y+Rsin(θ)≥78 or Y+Rsin(θ)≤9
Repeat X+Rcos(θ)≤150 and X+Rcos(θ)≥9 and Y+Rsin(θ)≤78 and Y+Rsin(θ)≥9

As r doesn't need to be accurate past whole numbers, this code works. However, it's quite slow (and I guess you could say pretty "BASIC"...) and I'm having trouble thinking of a faster method. Any suggestions?
You already have X+Rcos(θ)=150 to calculate when the point hits one of the sides. It's positive when R is traveling towards that side. Solve this for R, then you want the minimum positive value of the four formulas.
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