Heights and Distances Practice Test 2

Question : 4 of 24

Marks: +1, -0

As observed from the top of a 135 m tall lighthouse, the angles of depression of two shipsapproaching it are 45° and 60°. If one ship isdirectly behind the other, find the distancebetween the two ships.

${135(√3-1)}/√3m$
${135(√3+1)}/√3m$
${130(√3-1)}/√3m$
All of the above
None of these

Validate

Solution:

In ΔABC,

135/x=\tan60°=√3

⇒x=135/√3

......(1)
In ΔABD,

135/{x+y}=\tan45°=1

⇒x+y=135

⇒y=135-x

⇒y=135-135/√3

⇒y={135(√3-1)}/√3

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