Question

Two vertical poles of different heights are standing 20m away from each other on the same level of the ground. The angle of elevation of the top of one pole from the foot of the other is 60° and the angle of elevation of the top of the other pole from the foot of the first pole is 30° . Find the difference in the heights of the two poles.

Answer 1

Answer:

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Answer 2

given two poles $20m$ apart and angles of elevation from foot of one to top of another pole, find the difference in their heights

Explanation:

1. let the shorter pole be denoted be 'A' and its height be 'a'
2. let the longer pole be denoted be 'B' and its height be 'b'
3. let the difference in heights be 'x', the we have                                                                                 $b-a=x$      ---(a)
4. let the distance apart between the poles be $d=20m$
5. the angle of elevation for pole 'A' from foot of pole 'B' be $30$° then we have,        $tan30$°$=\frac{a}{d}=\frac{1}{\sqrt{3} }$            $->a=\frac{20}{\sqrt{3}}$    
6. the angle of elevation for pole 'B' from foot of pole 'A' be $60$° then we have,        $tan60$°$=\frac{b}{d}=\sqrt{3} \ \ \ \ \ \ \ \ \ \ ->b=20\sqrt{3}$  
7. putting values of 'a' and 'b' in (a) we get,                                                                        $x=20\sqrt{3} -\frac{20}{\sqrt{3} } \\x=\frac{40}{\sqrt{3}}m$------->ANSWER