A drone camera is used to shoot an object P from two different positions R and S along the same vertical line QRS. The angle of depression of the object P from these two positions are 35° and 60° respectively as shown in the diagram. If the distance of the object P from point Q is 50 metres, then find the distance between R and S correct to the nearest meter

Subject:
Math
Author:
moriah
Created:
1 year ago

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Answer:

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Author:

arielwf6m
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Given:

A drone camera is used to shoot an object P from two different positions R and S along the same vertical line QRS. The angle of depression of the object P from these two positions are 45° and 60° respectively .The distance of the object P from point Q is 50 meters ,

To Find:

Distance between R and S

Step-by-step explanation:

In ΔPQR

[tex]tan(45)=RQ\div PQ=RQ\div 50\\1=RQ\div 50\\RQ=50[/tex]

In ΔPSQ

[tex]tan(60)=SQ\div PQ=(SR+RQ)\div PQ=(SR+50)\div 50\\\sqrt{3}= (SR+50)\div 50\\50\times \sqrt{3} =SR+50\\SR=50\times(\sqrt{3}-1 )\\SR=50\times 0.732=36.6\\[/tex]

So answer to the nearest integer is 37m.

The final answer is 37m

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elviserickson
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