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प्रश्न
As observed from the top of a 100 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. [Use `sqrt3` = 1.732]
उत्तर
Let AB be the lighthouse and two ships be at point C and D.
In ΔABC,
tan 45° = `(AB)/(BC)`
⇒ 1 = `100/(BC)`
⇒ BC = 100 m
In ΔABD,
⇒ tan 30° = `(AB)/(BD)`
⇒ `1/sqrt(3) = 100/(100 + CD)`
⇒ 100 + CD = `100sqrt(3)`
⇒ CD = `100(sqrt(3) - 1)`
⇒ CD = 100(1.732 – 1)
⇒ CD = 100 × 0.732
⇒ CD = 73.2 m
Therefore, the distance between the two ships is 73.2 m.
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