ICSE Class X Math 2016 Solved Paper

Question : 29 of 57

Marks: +1, -0

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.

\;\;\text " Given : "\; {\CD}=1500 {\m}, ∠ {\EDA}=30^{∘}, ∠ {\EDB}

\;=45^{∘}

△ {\DBC}

\;\tan 45^{∘}=\;{D C}/{B C}=\;{1500}/{B C}

\;1=\;{1500}/{ {\BC}}

\;⇒ \;\; B C=1500 {\m}

△ {\ADC}

\tan 30^{∘}\;=\;{ {\DC}}/{ {\AC}}

\;{1}/{{√{3}}}\;=\;{1500}/{ {\AB}+ {\BC}}

{\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}

Go to Question:

Prev Question

Next Question