Greenwood press

TRIANGLE TRIGONOMETRY
149
The height of a hill can be determined
using the law of sines and right-triangle
trigonometry by measuring the angles of
elevation at points A and B, and the dis-
tance between points A and B.
The length of a newly paved road can be
determined using the law of cosines, given
the length of two adjacent roads and angle
C—the angle between the existing road.

---

Triangle trigonometry has many other applications that help find unknown
lengths or angle measurements. For instance, paintings, motion pictures, and
televisions have ideal viewing distances in order to create the greatest possible
image from the eye. The triangle is formed between the view and the top and bot-
tom (or the sides) of the viewing object.
Astronomers use triangle trigonometry to determine distances and sizes of
objects. For example, the distance from the earth to the moon, and earth to the sun,
can be found by identifying their angles from the horizon during an eclipse. The
height of a solar flare can also be determined by measuring the angle from the sun
to the tip of the flare, and using distance information about the earth and sun.
online sources for further exploration
Astronomy and geography

Cable television

Civil engineering and navigation

Height of a tree


Inclined ramp

Pipe flow

Saturn’s mass and distance from earth

Surveying


▲
▼
▲
VARIATION
When two quantities increase proportionally, we say they are directly related.
Mathematically, the two quantities 
x and y must be related as y = kx, where k is
a nonzero constant called the constant of variation. The formula for circumfer-
ence
c of a circle in terms of radius r is c = 2πr. The constant of variation is 2π.
The independent variable can be a power. The area of a circle is directly related
to the square of the radius, 
A = πr
2
. The constant of variation is 
π. Kepler’s