From a balloon ....

Question

From a balloon 734 feet high, the angle of depression to the ranger headquarters is 70°31'. How far is the headquarters from a point on the ground directly below the balloon(to the nearest foot)?

Answer 1

If you draw a sketch you can make out that y/x = tan(θ) where y is the vertical distance and x is the horizontal distance and Θ is the angle of depression.  We want x, so

 

x = y/tan(Θ) = 734 ft / tan(70+31/60)