SOLUTION: A hot air balloon is floating above a straight road. To estimate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mi
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Question 857246: A hot air balloon is floating above a straight road. To estimate 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 20 degrees and 24 degrees. How high is the balloon?
Struggling with this question please help Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! 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
