From a balloon that is 1000 m above the ground, an object is sighted on the ground at angle of depression 41.

Question

An observer in a second balloon, positioned at 600m above the ground views the same object at angle of depression of 28. Calculate the distance between two balloons.

Answer 1

There is not enough information to solve this. But let's start by figuring out how far the object is from a point directly beneath each balloon. This is simple. It is a distance x such that tan(theta) = h/x, so s = h / tan(theta), where h is the balloon's altitude and theta is the angle of depression. So if the balloon at 1000 m is balloon 1 and the balloon at 600 m is ballon 2, we have x1 = 1000 / tan(41) = 1150 m and x2 = 600 / tan(28) = 1128 m.

However, we have no idea how the balloon are oriented. We know that they are 400 m apart vertically , because one is at 1000 m and the other at 600 m, and 1000 - 600 = 400 m. But with one 1150 m from the object, horizontally, and the other 1128 m away from the object, also horizontally, the horizontal distance between the two balloons could be anywhere from 1150 - 1128 = 22 m (if they are on the same side of the object) to 1150 + 1128 = 2278 m apart horizontally (if they are on opposite sides of the object). If you had enough information to get the horizontal separation, call it d, then the actual distance between the balloons would be sqrt(400^2 + d^2), an application of the Pythagorean theorem.

Answer 2

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