Applications and Solving Right Triangles
•
Section 1.3
15
Example 1.13
A blimp 4280 ft above the ground measures an
angle of depression
of 24
◦
from its horizontal line of
sight to the base of a house on the ground. Assuming the ground is Fat, how far away along the
ground is the house from the blimp?
24
◦
4280
θ
x
Solution:
Let
x
be the distance along the ground from the blimp
to the house, as in the picture to the right. Since the ground and the
blimp’s horizontal line of sight are parallel, we know from elementary
geometry that the angle of elevation
θ
from the base of the house to
the blimp is equal to the angle of depression from the blimp to the
base of the house, i.e.
θ
=
24
◦
. Hence,
4280
x
=
tan 24
◦
⇒
x
=
4280
tan 24
◦
=
9613 ft
.
Example 1.14
An observer at the top of a mountain 3 miles above sea level measures an angle of depression of 2.23
◦
to the ocean horizon. Use this to estimate the radius of the earth.
r
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 Fall '11
 Dr.Cheun
 Calculus, Angles, Geodesy, Euclidean geometry

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