PreCalc
posted by John .
A hotair 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 24° and 27°. How high is the balloon? (Round your answer to one decimal place.)

We form 2 rt triangles with a common ver. side.
tan27 = h/x.
Eq1: h = X*tan27 = 0.5095X.
tan24 = h/(X+1).
h = tan24*(x+1).
h = 0.4452(x+1).
h = 0.4452x + 0.4452.
0.5095x = 0.4452x + 0.4452.
0.5095x  0.4452x = 0.4452.
0.0643x = 0.4452.
X = 0.4452 / 0.0643 = 6.92. Miles.
h = x*tan27 = 6.92*tan27 = 3.5 Miles.