Problema Solution
The angle of depression of a car from an air balloon basket is 40 degrees. The balloon is directly over a water tower that is 5km from the car. Find the altitude of the balloon.
Answer provided by our tutors
let a = the altitude of the balloon
make a drawing on the balloon and the car - you will notice that the balloon, the car and the water tower can be considered as vertices (corners) of a right triangle with one acute angle equal to 40 degrees, and the right angle at the water tower vertex.
the altitude is the length of the side of the triangle that lies opposite the 40 degrees angle (the car vertex)
now we can write
tan (40) = a/5
by solving we find
a = 4.195 km
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the altitude of the balloon is 4.195 km.