A vertical tower standing on a levelled field is mounted with a vertical flag staff of length 3 m. From a point on the field, the angles of elevation of the bottom and tip of the flag staff are `30^(@)` and `45^(@)` respectively. Which one of the following gives the best approximation to the height of the tower?

Options

A. 3.90m
B. 4.00m
C. 4.10m
D. 4.25 m

Answer

C

Explanation

as `angleCPA=45^(@)`

so `AC=AP=x+3`
`tan 30^(@)=(AB)/(AP)=(x)/(x+3)`
`(1)/(sqrt(3))=(x)/(x+3)`
`x+3=sqrt(3)x`
`x=(3)/(sqrt(3)-1)xx((sqrt(3)+1))/((sqrt(3)+1))`
`x=(3xx2.73)/(2)=(8.19)/(2)=4.095m ~~4.1m`