Answer: the distance of the boat from the foot of the lighthouse is
290.8 feet
Step-by-step explanation:
The scenario is represented by the right angle triangle shown in the attached photo.
Looking at triangle ABC, the height of the light house above sea level represents the opposite side of the right angle triangle.
Angle A = 11.1° since it is alternate to the angle of depression.
To determine AB, the distance of the small boat from the base of the lighthouse, we would apply
the tangent trigonometric ratio which is expressed as
Tan θ, = opposite side/adjacent side. Therefore,
Tan 11.1 = 57/AB
AB = 57/Tan 11.1 = 57/0.196
AB = 290.8 feet
