ICSE Class X Math 2016 Solved Paper
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Question : 29
Total: 57
An aeroplane at an altitude of 1500 metres finds that two ships are sailing towards it in the same direction. The angles of depression as observed from the aeroplane are 45 ∘ and 30 ∘ respectively. Find the distance between the two ships.
Solution:
Let D is the aeroplane. A and B are two ships.
Given : CD = 1500 m , ∠ EDA = 30 ∘ , ∠ EDB = 45 ∘
In△ DBC ,
tan 45 ∘ =
=
1 =
⇒ B C = 1500 m
In△ ADC ,
tan 30 ∘ =
=
AB + BC = 1500 √ 3
AB = 1500 √ 3 − 1500
AB = 1500 ( √ 3 − 1 )
= 1500 ( 1 ⋅ 73 − 1 )
= 1500 × 0.73
$ \;=1095 {\m} .
$
Hence, distance between two ships= 1095 m .
In
In
$ \;=1095 {\m} .
$
Hence, distance between two ships
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