Practical_Antenna_Handbook_0071639586

A p p e n d i x A : U s e f u l M a t h 717
The other important point to take away from Eq. (A.3.6) is that the higher the frequency
f of the sinusoidal driving force, the larger the coefficient of the acceleration
terms in front of the sin or cos term. As we discuss in Chap. 3, electromagnetic radiation
is caused by accelerated charges; it is clear from this equation that the propensity for EM
radiation increases with increasing frequency f.
A.4 Triangles
In plane geometry we find three kinds of triangles, as shown in Fig. A.4.1:
• Equilateral (where all three sides are of equal length)
• Isosceles (where two sides are of equal length)
• Scalene (where no two sides are the same length)
All three types share a common trait: The sum of their three interior angles (a, b, and g)
is always 180 degrees.
We can also categorize triangles by their interior angles:
• Acute (where no interior angle is 90 degrees or greater)
• Right (where one interior angle is exactly 90 degrees)
• Obtuse (where one interior angle is greater than 90 degrees)
Right Triangles
In a right triangle, one angle is always 90 degrees, so the sum of the other two angles
must also be 90 degrees. The side opposite the right angle is perpendicular to neither of
the other two sides, and it is always the longest side of the three; it is called the hypotenuse.
If we place a right triangle on an x-y grid so that the two perpendicular sides are on
the x and y axes as shown in Fig. A.4.2, the relative lengths of the sides and the three
interior angles are related as shown in the figure.
For a right triangle—and only for a right triangle—the square of the hypotenuse is
equal to the sum of the squares of the other two sides:
2 2 2
h = a + b
(A.4.1)
a a a a
a
c
Figure A.4.1 Types of plane triangles.
a
(A)
Equilateral
b
(B)
Isosceles
b
(C)
Scalene