A man at A observes the angle of elevation of a balloon to be 30 degrees . He then walks 1000 meters towards the balloon to a point B and finds the elevation to be 60 degrees. If the balloon has a height of H meters and the man has X meters still to walk before he is directly under the balloon
, we can set up the following equations:
At point A:
H/tan(30) = x
At point B:
(H + x)/tan(60) = 1000 + x
Solving the first equation for H gives:
H = x*tan(30)
Substitute this into the second equation gives:
(x*tan(30) + x)/tan(60) = 1000 + x
(x*(tan(30) + 1))/tan(60) = 1000 + x
x = (1000*tan(60))/(tan(30) + 1 - tan(60))
x = 577.4
Therefore, the man has 577.4 meters still to walk before he is directly under the balloon.