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Trigonometry in the Real World 347
Figure 23-7
A radar display
shows azimuth
and range in
navigator’s polar
coordinates.
a narrow beam. The waves strike objects at various distances. The greater the distance
to the target, the longer the delay before the echo is received. The transmitting antenna
is rotated so that all azimuth directions can be observed.
A typical circular radar display is shown in Fig. 23-7. It uses navigator’s polar coordinates.
The observing station is at the center of the display. Azimuth is indicated in
degrees clockwise from north and is marked around the perimeter of the screen. The
distance, or range, is indicated by the displacement of the echo from the center of the
screen.
LAWS OF SINES AND COSINES
When you want to find the position of an object using trigonometry, or when you want
to figure out your own location based on bearings, it helps to know two important rules
about triangles.
The first rule is called the law of sines. Suppose a triangle is defined by three points P,
Q, and R. Let the lengths of the sides opposite the vertices P, Q, and R be called p, q,
and r, respectively (Fig. 23-8). Let the angles at vertices P, Q, and R be p
, q
,and r
,
respectively. Then the lengths and angles are related in this way:
p / (sin p
) q / (sin q
) r / (sin r
)