OPTIMUM
M A S C H I N E N - G E R M A N Y
General information about CNC
Version 1.1.6 dated 2014-10-16
Page 53
Original operating instructions
F150
GB
Rectangular triangle
The rectangular triangle has a special meaning in the analytic geometry as the sides of such a
triangle are having a definite mathematic relation to one another.
On a rectangular triangle the single sides are specially named.
The longest side is located opposite to the right angle and is named hypotenuse.
The two sides of the triangle which are forming the right angle are named cathetus.
The side opposite the angle a is named opposite leg.
The side adjacent to the angle a is named adjacent leg.
On a rectangular triangle the right angle is described by an quarter circle and a point in the
angle.
In a rectangular triangle it applies:
In a rectangular triangle you can calculate the missing leg if the other leg lengths are known. To
do so, use the Pythagorean theorem.
The Greek Pythagoras (from about 580 to 496 before Jesus Christ) had been the first person to
prove the following mathematic relation which had later on been named the Pythagorean theo-
rem.
The sum of the cathetus square is equal to the hypotenuse square and expressed as a equa-
tion:
a² + b² = c²
4.4
Trigonometric functions
The trigonometric functions describe the relations between the angles and the sides of a rec-
tangular triangle. With the help of these trigonometric functions it is possible to calculate
unknown leg lengths with an unknown angle and a known leg. It is depending on which side
and which angle are known in order to choose the appropriate trigonometric function e.g. the
sinus function, the cosine function or the tangent function.
For the calculation of unknown legs the corresponding equation needs to be transformed as
described in the following example:
Known are: the angle and the length of the adjacent leg
Looking for: the length of the opposite leg
It applies: tan alpha = opposite leg / adjacent leg
The results is:
opposite leg = adjacent leg x tan alpha
a
b
c
