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  • There are two poles, one each on either bank of a river just opposite to each other. One pole is 60 m high. From the top of this pole, the angle of depression of the top and foot of the other pole are <img alt="30^{\circ}" src="https://entrancecor

There are two poles, one each on either bank of a river just opposite to each other. One pole is 60 m high. From the top of this pole, the angle of depression of the top and foot of the other pole are 30^{\circ} and 60^{\circ} respectively. Find the width of the river and height of the other pole.

 

 

 
 
 
 
 

Answers (1)

Given Poles AB and CD
width of river = AC
Length of AB = 60 m

To find \rightarrow AC and CD
In \triangle ABC
\tan 60^{\circ}= \frac{AB}{AC}\Rightarrow \sqrt{3}= \frac{60}{AC}
\Rightarrow AC= \frac{60}{\sqrt{3}}= 20\sqrt{3}\, m
In \triangle BED
\tan 30^{\circ}= \frac{BE}{ED}\Rightarrow \frac{1}{\sqrt{3}}= \frac{BE}{AC}   (\therefore ED= AC)
\Rightarrow BE= \frac{AC}{\sqrt{3}}= \frac{20\sqrt{3}}{\sqrt{3}}= 20 m
\Rightarrow BE= 20 m
AE= AB-BE
         60-20= 40 m
\Rightarrow AE= CD= 40m
Length of pole, CD = 40 m
width of river, AC = 20\sqrt{3} m 

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Safeer PP

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