Question

Two tracking stations 525 m. apart measure angles of elevation of a weather balloon to be 73.5 degree and 54.2 degree. How high is the balloon at the time of the measurement? Round to the nearest meter.(show your work)

Answer 1

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Answer:

516 m or 1235 m

Explanation:

The height of the balloon depends on the geometry of the problem. Assuming the stations are in line with each other and the balloon, there are a couple of possible configurations that satisfy the problem description. They are shown in the attachment.

If the balloon is between the stations, the height is 516 m.

If the balloon is not between the stations, the height is 1235 m.

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A graphing program solves the problem nicely. If you want to solve it algebraically, You can write equations for the horizontal distance from each station to the balloon.

d1 = h/tan(54.2°)

d2 = h/tan(73.5°)

In one of the possible geometries, ...

d1 + d2 = 525

h(1/tan(54.2°) +1/tan(73.5°)) = 525

h = 525tan(54.2°)tan(73.5°)/(tan(54.2°) +tan(73.5°)) ≈ 516.0 . . . meters

In the other possible geometry, ...

d1 -d2 = 525

h(1/tan(54.2°) -1/tan(73.5°)) = 525

h = 525tan(54.2°)tan(73.5°)/(tan(73.5°) -tan(54.2°)) ≈ 1235.3 . . . meters

The balloon could be 516 or 1235 meters high.