EXAMPLE 12 Find the distance from the eye at which
a coin of diameter 2 cm should be held so as just to conceal
the full moon, whose angular diameter is 31'.
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Answer:
Suppose the coin is kept at a distance r from the eye to hide the moon completely.
Let E be the eye of the observer and let AB be the diameter of the coin.
then arcAPB= diameter AB=2.2cm
Now θ=30
0
(
60
30
)=(
2
1
.
180
π
)=(
360
π
)
∴θ=
radius
arc
⇒
360
π
=
r
2.2
⇒r=
π
2.2×360
⇒r=
22
2.2×252×7
=252
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