MACHINE SHOP CALCULATION - OD1640 - LESSON 2/TASK 3
rpm in the pulley or gear train of military machinery and vehicles.
Task 3 will describe the processes for solving problems through
triangulation, otherwise known as trigonometry. Trigonometry is essentially
that branch of mathematics which deals with the relations existing between
the sides and angles of triangles. In this task only right triangles will
be discussed. A right triangle is a triangle that contains one 90,, angle
and two other lesser angles for a total of 180,, or half the number of
degrees in a circle, which contains 360,,.
This process will assist the machinist in determining the pitch or angle of
screw threads, gear teeth, and tapers for parts that must be fabricated for
items not normally available through supply channels, or in an emergency in
a combat situation.
Before going into the solving of trigonometric
problems, let's first review the trigonometric functions which are the basis
for solving these types of problems.
For any given acute angle in a right triangle, certain ratios exist
among the sides.
These ratios are called "trigonometric functions." They
determine sides and angles in a right triangle. To this end, the sides of a
right triangle are given certain names to indicate their relation to the
Thus, in any right triangle, such as shown in figure 12 on the
following page, the side "c," which is opposite to the right angle "C," is
called the "hypotenuse"; side "a" is opposite angle "A" and is called the
"opposite side"; side "b," is adjacent to angle "A" and is called the
"adjacent side." Notice, however, that when the sides refer to angle "B,"
side "b" is the opposite side and side "a" is the adjacent side. However,
the hypotenuse, the longest side, is always called the hypotenuse with
reference to either angle.
In this triangle, it is possible to show six different ratios of the
sides. They are a/c, b/c, a/b, b/a, c/b, and c/a. An explanation of these
ratios follows using the ratio a/c as an example. This explanation is also
applicable to the other ratios; a/c means the same as "a" divided by "c,"