If the height of the tower is h, then
h/18 = tan60°
from the new position, at a distance x,
h/x = tan40°
If we label a diagram with
T = base of tower
A = initial position
B = final position of man
If T is at (0,0) then B is at (h,k) where
h = -18-25sin∅
k = 25 cos∅
and h^2 + k^2 = x^2
A man standing 18m due west from the base of a vertical tower observes that the angle of elevation of the is 60⁰. He then walks a distance of 25m in a direction of N ∅⁰ W (where ∅ is acute) and observes that the angle of elevation is now 40⁰. Calculate, correct to one decimal place
A) The height of the tower
B) The distance of the man from the tower in the second position of observation
C) The value of ∅.
1 answer
1 answer