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=1500m,EDA=30,EDB =45

In DBC ,
tan45=
DC
BC
=
1500
BC

1=
1500
BC

BC=1500m
In ADC ,
tan30=
DC
AC

1
3
=
1500
AB+BC

AB+BC=15003
AB=150031500
AB=1500(31)
=1500(1731)
=1500×0.73
$ \;=1095 {\m} .
$
Hence, distance between two ships =1095m .
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