Practical_Antenna_Handbook_0071639586

718 A p p e n d i x A : U s e f u l M a t h
y
hypotenuse
h
b
Symbol indicating a
right triangle
a
h 2 = a 2 + b 2
a = h sin
b = h sin
x
Figure A.4.2 Right triangle relationships.
so it follows that
h = a 2 + b 2 and a = h 2 − b 2 and b = h 2 − a
2
(A.4.2)
Sometimes it is helpful to think of the sides a and b as the projections of h onto the x
and y axes, respectively. For instance, if the sun is directly overhead, a is the shadow
projected by a stick having the length and orientation of h onto the ground directly beneath
it.
The sides and interior angles of a right triangle are related by the following equations:
sin α = a h or a = h sin α
(A.4.3a)
sinβ = b h
or b = h sin β (A.4.3b)
For completeness, we list the following additional relationships in a right triangle:
cosα = b h
or b = h cosα (A.4.3c)
cosβ = a h
or a = h cosβ (A.4.3d)