Question

A helicopter flies horizontally at 100 kmph. An observer notices that it took 20 seconds for the helicopter to fly from directly overhead to being at an angle of elevation of 60 degrees. Find the height of the helicopter above the ground.

Answer 1

We must convert 100 km per hour to seconds.

100 km        1 hr             1 km
---------- * --------------- = -----------
  1 hr         3600 sec       36 sec

How far did the copter fly horizontally in 20 sec at the rate 1 km / 36 sec?

20 sec     1 km
--------- * ---------- = 0.556 km 
    1         36 sec

So the horiz distance flown by the plane in those 20 sec was 0.556 km.  This horiz. distance forms the side adjacent to the 60 degree angle.  We need to find the length of the side opposite the 60 degree angle:

                       opposite side      height of copter
tan 60 deg = -------------------- = -----------------------
                       adjacent side                0.55 km
                                                                       
Solving for the height of the copter,   height =  (0.55 km)(tan 60 deg) =

(0.55 km)(1.73) = 0.96 km.  The copter was 0.96 km above ground.