A hotair balloon is floating above a straight road To calcul

A hot-air balloon is floating above a straight road. To calculate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 16degree and 18degree. How high (in feet) is the ballon?

Solution

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 18 = h/x
h = x tan 18
similarly
h= (x+1) tan 16 for second post which is a mile away from 1st post
xtan 18 = (x+1) tan 16

x(tan 18 - tan 16) = tan 16
x= tan 16/(tan 18-tan 16)
x= 7.51 miles

now height h = x tan 18 = 2.441 miles = 12888.48 feet

since 1 mile = 5280 feet