An aircraft which is maintaining a constant altitude of 1000 meters is travelling directly away from an observer. At a particular instant the sngle of elevation is 52 degrees and 12 seconds later the angle of elevation is 16 degrees. Find the distance travelled in this time.

Question

An aircraft which is maintaining a constant altitude of 1000 meters is travelling directly away from an observer. At a particular instant the sngle of elevation is 52 degrees and 12 seconds later the angle of elevation is 16 degrees. Find the distance travelled in this time. 
(Use sine rule)

HELP!!!!!!!!

Steve · Answer

Hmmm. I don't see an obvious application of the law of sines here. However, if we consider the distance directly to the plane, and call the first one x and the second one y, then

1000/x = sin52°
1000/y = sin16°
Then we want the distance z given by the law of cosines,
z^2 = x^2+y^2-2xy cos(52-16)°

Or,

z/sin36° = x/sin16° = y/sin128°