Expert: Sherry Wallin - 12/4/2009

Question
QUESTION: By using a right triangle with a base created From point A to pint B (point B is next to the 90degree angel) and the hypothenuse is created by Point A to Point X so so far A to B is base and A to X is hypothenuse therefore B to X is last side Next the line A to B and line A to X create angle T and there is another point which is C and C is inbetween A to B which creates angle 2T so so far the base and hypothenuse creates angle T and C to B and C to X creates angle 2T therefore creating a smaller triangle and i need you to prove that Line A to C is equal to Line C to X.
         X
         /!
         / !
         /  !
         /   !
         /    !
        /     !
       /      !
      /       !
     /        !
    /         !
   /          !
  /          !
 /          !
/          !
/T______/2T____!
A        C     B

ANSWER: Please draw a diagram and save it as jpg or png file and attach it and I will help you with your problem.

Math Prof

---------- FOLLOW-UP ----------

QUESTION: By measuring the angle created (frpm A to B in diagram) and the object (from A to X) track how far it is from point A to point C. The distance to X from C is the same distance as A to C. This is what i need to prove.

Answer
Thanks for the drawing.

Notice since m < BCA = 2T that m < CXB = 90-2T since triangle ABC is a right triangle. Also m < AXC is T for a couple of reasons.

One reason is because the measure of an external angle of a triangle equals the sum of it's non adjacent interior angles. One of the non adjacent interior angles measures T so the other has to be T also in order to equal 2T the measure of the external angle.

Another reason is that since m < CXB is 90-2T and triangle BAX is also a right triangle then m < AXB = x + 90-2T = 90-T and solve for x you get x = T.

Using the law of sines on triangle CAX we get sin T/AC = sin T/CX which heavily implies that AC = CX which is what you wanted proved.

Divide both sides by sin T (this is ok since the only time the sine of an angle is 0 is when the angle is 0 deg or 180 deg and this won't happen in a triangle). Then you have 1/AC = 1/CX, either cross multiply to get AC = CX or use the fact that if two fractions are equal then their reciprocals are also equal.

Math Prof