Answer: 434.35 feet
Step-by-step explanation:
The angle of depression from the lighthouse is the angle of elevation from the boat. The line of sight from the top of the lighthouse, when depressed, becomes an alternate interior angle of two parallel lines, the line of sight from the top and the boat's movement.
From the boat's standpoint, which is what we want anyway, there is a right triangle, with the distance from the lighthouse the adjacent side, the opposite is 200,' and the boat the point desired.
tan 18.33 (33 minutes is 33/60 of a degree)=200/x
x=200/tan 18.33=592.58 feet
Nearer, the angle of elevation increases as the adjacent side gets smaller relative to the opposite side.
tan 51.33 (33 minutes is 33/60 of a degree)=200/x
x=200/tan 51.33=158.23 feet
That difference is 434.35 feet
Alternatively:
tan(51 33')= 200/base1
base1= 158.802
tan(18 33')=200/base2
base2=596.008
The distance travelled=596.008-158.802 =438m
