posted by Candy

A balloon isin the vertical plane of two consecutive milestones of a road. The angles of depression of the stones as viewed from the balloon are 15 degrees and 17 degrees. Find the height of the balloon if (a) the stones are on opposite sides of the balloon, (b) the stones are on the same side of the balloon.

1. Candy

I'm almost getting ready 2 go 2 sleep and i really really need help. Just show me how to set the problem up and I can just solve it from there. Thanks :)

2. Steve

If the balloon is between the stones, then: Let the balloon be x away from the first stone, and 1-x away from the other

h/x = tan 15° = .268
h/(1-x) = tan 17° = .306
.268x = .306(1-x)
x = .533
1-x = .467
height = .1428 mi = 754 ft

If the balloon is not between the stones, let it be x from the farther stone and x-1 from the nearer

h/x = tan 15° = .268
h/(x-1) = tan 17° = .306
.268x = .306(x-1)
x = 4.5
x-1 = 3.5
h = .268*4.5 = 1.206 mi = 6367 ft

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