The angle of elevation of the top of a flag post from a point 5 m away from its base is `75^(@)`. What is the approximate height of the flag post?

Options

A. 15m
B. 17m
C. 19m
D. 21m

Answer

C

Explanation

Let h be the height of the flag post where BC is the base.
In `DeltaABC`,
`tan 75^(@)=(AB)/(BC)=(h)/(5)`
`rArr tan (45^(@)+30^(@))=(h)/(5)`
`rArr (tan 45^(@)+tan 30^(@))/(1-tan 45^(@) tan 30^(@))=(h)/(5) " " (. :' tan (A+B)=(tan A + tan B)/(1-tan A tan B))`
`rArr (sqrt(3)+1)/(sqrt(3)-1)=(h)/(5)rArrh= ((sqrt(3)+1)^(2))/((sqrt(3))^(2)-(1)^(2))xx5`
`rArr h=5 ((3+1+2sqrt(3))/(3-1))=5(2+sqrt(3))`
`=5xx3.732=18.660`
=19m (approx,)