Two poles are 10 m and 20 m high. The line joining their tops makes an angle of `15^(@)` with the horizontal. What is the approximate distance between the poles?

Options

A. 36.3 m
B. 37.3 in
C. 38.3 m
D. 39.3 in

Answer

B

Explanation

`tan 15^(@)=DE//AE`
`AE=10 cot 15^(@) " " ...(1)`
`cot (15^(@))=cot (45-30^(@))`
`=(cot 45^(@) cot 30^(@)+1)/(cot 30^(@)-cot 45^(@))`

`cot 15^(@)=(1.sqrt(3)+1)/(sqrt(3)-1)=2+sqrt(3)`
Putting cot `15^(@) ` in eq(1)
`AE=10 cot 15^(@)`
`=10(2+sqrt(3))`
`=10(3.73)=37.3m`