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. 35.3m
B. 37.3m
C. 41m
D. 44m

Answer

B

Explanation

Let AC and ED be two poles of height 20m and 10m respectively.
Let `angleAEB=15^(@)`
To find : DC.

Now, `AB=AC-BC=AC-ED=20-10=10m`.
Now in `Delta ABE " " (.:' BC=ED)`
`tan 15^(@)=(AB)/(BE)`
`rArr tan (45^(@)-30^(@))=(10)/(BE)`
`rArr (tan 45^(@)-tan 30^(@))/(1+tan 45^(@)tan 30^(@))=(10)/(BE) " " (.:' tan (A-B)=(tan A - tan B)/(1+tan A tan B))`
`rArr (sqrt(3)-1)/(sqrt(3)+1)=(10)/(BE)`
`rArr BE=10((sqrt(3)+1)/(sqrt(3)-1))=(10xx(sqrt(3)+1)^(2))/(2)`
(By rationalizing)
`5(3+1+2sqrt(3))=5(4+2xx1.73)=5(4+3.46)`
`rArr CD=BE=5xx7.46=37.3 m`