A plane is flying at a constant altitude and speed of 500km/hr. At a certain point, the angle of depression from the airplane to a lighthouse on an island in the distance is 6 degrees. After 12 minutes, as the plane continues to approach the lighthouse, the angle of depression becomes 15 degrees. How long will it take for the plane to be directly above the lighthouse from the point where the angle of depression was 6 degrees

Answer 1

in 12 minutes, the plane has gone 100km
So, reviewing your basic trig functions, you should see that at height h,

h cot 6° - h cot 15° = 100
h = 17.29km

Now the distance to the point over the lighthouse is

h tan75° = 64.53km

At 500 km/hr, that will take 7.75 minutes to cover