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

#CBSE 10 Class
#Some Applications of Trigonometry
#Maths
#School

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 = $20\sqrt{3} m$