Graphics Programs Reference
In-Depth Information
The Pythagorean Theorem
Here's something else that we'll use all the time in various ways. Named after the
Greek philosopher Pythagoras, the Pythagorean theorem states that for a right triangle,
the square of the hypotenuse is equal to the sum of the squares of the other two sides.
What's a hypotenuse? It's the longest side, the one opposite the right angle. This is one
of the foundations of trig and appears many times in all kinds of situations.
b
c
2
= a
2
+ b
2
a
Figure 5.10
The Pythagorean theorem
Figure 5.11 illustrates some common right triangles and the proportional relationships
of their short sides to their hypotenuses.
5
2 = 1.414
1
3
4
1
45
o
triangle
3,4,5 right triangle
5
2
1
1
2
3 = 1.732
30
o
-60
o
triangle
“golden” triangle
Figure 5.11
Common triangles and the ratios of their sides
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