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16
Chapter 1
•
Right Triangle Trigonometry
§1.3
Example 1.15
O
A
B
α
As another application of trigonometry to astronomy, we will Fnd the distance
from the earth to the sun. Let
O
be the center of the earth, let
A
be a point
on the equator, and let
B
represent an object (e.g. a star) in space, as in the
picture on the right. If the earth is positioned in such a way that the angle
∠
OAB
=
90
◦
, then we say that the angle
α
=
∠
OBA
is the
equatorial parallax
of the object. The equatorial parallax of the sun has been observed to be ap
proximately
α
=
0.00244
◦
. Use this to estimate the distance from the center of
the earth to the sun.
Solution:
Let
B
be the position of the sun. We want to Fnd the length of
OB
.
We will use the actual radius of the earth, mentioned at the end of Example
1.14, to get
OA
=
3956.6 miles. Since
∠
OAB
=
90
◦
, we have
OA
OB
=
sin
α
⇒
OB
=
OA
sin
α
=
3956.6
sin 0.00244
◦
=
92908394 ,
so the distance from the center of the earth to the sun is approximately 93 million miles
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 Fall '11
 Dr.Cheun
 Calculus, Trigonometry

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