# pre-calc

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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?

• pre-calc -

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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