Find Point On Rect Edge

  1. Overview

    I've been struggling at this problem for about 3 days now. I've posted it on a couple forums will no answers, so maybe I'll get a solution here. Thanks in advance!


    Plain Diagram:

    Known: A, B, C, P, R, T, Z, h, w

    Need: D, E, F; Length of dcef and ef segments

    Y axis is inverted!!

    (0,0) is at top left corner of rectangle

    Known Data
    h = 600
    w = 800

    C is at (w/2,h2) = (400,300)
    R is at (400,0)
    P is at (400,600)

    A is at (534,88)
    B is at (740,296)
    T is at (534,0)
    Z is at (534,600)

    ∠TAB = 135°
    ∠ZAB = 45°

    ∠RCE = ∠TAB
    ∠PCE = ∠ZAB

    Problem Solving
    ∠ZFE = 90 - ∠PCE
    ∠ZFE = 45°

    segCP = segRC = 400
    segCF = sin(∠PCF) × segCP
    segCF = sin(45) × 400
    segCF = 282.8427125

    The Question!

    Now all I really need is the length of segEF to solve the problem, since we know that segDE = segAB.

    So segDF = segDE + segEF

    Can anyone help me get segEF?

    Something to note: This is a real-world problem where ∠TAB will be anywhere from 0° to 360°, which in-turn would affect what side and position F would be. And ∠RCF always = ∠TAB
  2. jcsd
  3. Anyone? :S
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