Question

There are two boats together either side of lighthouse 200ft high. The angles of depression of the boats from the top of the lighthouse are 40° and 50° respectively.If the boats and lighthouse are in one straight line, calculate the distance between the boats.

Answer 1

Figure is in the attachment.

Let A and B be the position of two boats (figure)

Let PM be the lighthouse such that PM =100m

Let AM =x and BM =y

In ΔAPM,  

PM

AM

​  

=cot30  

∘

 

⇒  

100

x

​  

=  

3

​  

⇒x=100  

3

​  

m

Similarly in Δ BPM,

PM

BM

​  

=cot45  

∘

⇒  

100

y

​  

=1⇒y=100m

∴ Required distance, AB=x+y

=100  

3

​  

+100=100(  

3

​  

+1)m=273.2m

Hope it helps.

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