A hot air balloon is floating above a straight road. To estimate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 20 degrees and 24 degrees. How high is the balloon?

Answer:3.677 milesStep-by-step explanation:First we have to know that the distance between two consecutive milestone is 1mile, I have attached a diagram representing the problem, point C being the point of the balloon and point A and point B being the points of the consecutive milestonesI labelled the horizontal length between the balloon and the first milestone x and the height of the balloon hFrom the diagram, we use the tan rule for right angle triangles to find x and hTan22=h/x Making her the subject of formula h=xtan22 (1)Similarly Tan20=h/(x+1)h=(x+1)tan20 (2)Putting (1) and (2) together We solve for x, and then input our value for in (1) to get the value for h, the solution is in the second picture I sent Note: tan rule says the tan of an angle is equal to the opposite side of the triangle(side directly facing the angle) divided by the adjacent side of the triangle( side of the triangle the angle is resting on) Angle of depression from C to B is also angle of elevation from B to C( alternate angle are equal)