Question 1121140: A tourist enjoying an early morning flight in a balloon finds the angle of depression of a farm shed is 28 degrees and 47 minutes and on descending vertically through 180 metres, finds the angle to be 12 degrees and 15 minutes. Find:
a) the height of the ballon at the first observation
b) the distance of the balloon from the shed at the second point of observation
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Draw this.
From the balloon, B, to the shed, S has a leg 180 m, vertically down from B, and from S, there is an angle of 12.25 deg (12d15m) back to B. The distance from S to B is the hypotenuse of a right triangle where the opposite side is 180.
sin 12.25=180/distance to shed
Distance=180/sin 12.25=848.3 m ANSWER b
The height at the first observation has an angle of 28.783 deg or 28d47m. The height is 180+x meters, the opposite leg and the adjacent leg is 848.3 m.
The tangent 28.783deg=opp/848.3
opp=848.3*tan 28.783=466.0 meters ANSWER a
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