Math 11
posted by Dylan .
From a weather balloon high in the air, the angle of depression of a ground marker is 27.8 degrees. If the balloon rises 345 m straight up the angle of depression from this higher point is 46.2 degrees. How high above the ground is the balloon?

If the marker is at distance x away from the spot just below the balloon, we have
h/x = tan 27.8
(h+345)/x = tan 46.2
Eliminate x to get
h/tan 27.8 = (h+345)/tan 46.2
Now just solve for h.