Question

two observers 3 miles apart and facing each other find that the angles of the elevation of a balloon in the same vertical plane with themselves are 28degree and 31 degree respectively.find the distance from the balloon to the observer located at the 31 angle?

Answers

Label the observers A and B, with point C on the line AB, directly below the balloon, at point D.

If x is the distance CB, then since AC+CB=3,

(3-x)tan28° = xtan31°
x = 1.4 miles.

Now, you want the distance DB, which is

x/DB = cos31°

DB = x/cos31° = 1.4/.857 = 1.63 miles

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