Question 857246
the distance between the posts is 1 mile

let x be the horizontal distance between the pole 1 and the ballon

height of balloon = h

tan 24 = h/x

h = x tan 24

similarly
h= (x+1) tan 20

xtan 24 = (x+1) tan 20

x(tan 24 - tan20) = tan 20

x= tan 20/(tan 24-tan 20)

x=4.48 miles

tan 24 = h/4.48 

tan 24 *4.48 = h

h=2 meters