Instructions

When programmers solve for tangent points, they usually start off knowing the

hypotenuse of the triangle they are working with, because it is the radius of the arc of

which they are solving for the start and stop points.

The hardest part of this part of the course isn’t solving a right triangle. It’s finding the

correct right triangle to solve to give you the answer to determine your tangent

coordinates that will determine the start and stop points of an arc. You’ll remember that I

told you that these points must be given to an accuracy of four decimal places in order to

work in unison with the computer. It has nothing to do with the accuracy you require, but

only with what our loyal computer requires.

I dug out my old calculator to solve these problems and then checked my answers against

what I had already calculated in AutoCad®. I’m going to assume you will be making the

same mistakes I did, so I’ll pass my thoughts on about the problems I had. When you’re

dealing with angles less than 10° changes are subtle and errors will not stand out. Be

absolutely sure that you are using the correct equation to work with the information that

you have available. All you need are two sides or a side and an angle other than 90°.

Figure 9

Rectangle, arc and tangent program

The first example I’m going to explain looks deceivingly simple and is typical of what

you have to start with, and believe me it isn’t easy, so pay attention. I started off this

drawing by putting a circle in a rectangle in no particular position on the X-axis and then

putting a 5° line against the tangent point of the circle. My next task was to figure out the

missing points with a calculator. The only practical way to accurately figure these points

out is with trig.

First we have to find and solve the missing values for the right triangles shown in Fig. 10

below. The key triangles are shown in solid black.