The angles of elevation of the top of a tower standing on a horizontal plane from two points of a line passing through the foot of the tower at distances 49 m and 36 m are `43^(@)` and `47^(@)` respectively. What is the height of the tower ?

Options

A. 40m
B. 42m
C. 45m
D. 47m

Answer

B

Explanation

AB=h (height of the tower)
BD=36m
BC=49m
`angleD=47^(@)`
`angleC=43^(@)`

Now, in `DeltaABD`,
`tan47^(@)=(h)/(36m) " " ...(i)`
and in `DeltaABC`,
`tan 43^(@)=(h)/(49m)`
`tan (90^(@)-47^(@))=(h)/(49)`
`:. cot 47^(@)=(h)/(49) " " ...(ii)`
Multiplying equations (i) and (ii)
`tan 47^(@). cot 47^(@)=(h)/(36)xx(h)/(49) = 1 = (h^(2))/(36xx49)`
`h=6xx7=42m`
`:. ` Option (b) is correct