Answer: 25.9 feet (approximate)
Step-by-step explanation
Refer to the diagram below.
We have this list of points
- A = base of the lifeguard's seat/tower
- B = the location of the lifeguard's eye
- C = the swimmer's location
- D = a point used to form the angle of depression
Angle DBC = 18° is the angle of depression. The diagram shown above problem 5 gives a good example of what "angle of depression" means.
Angle DBC = Angle ACB because of the alternate interior angle theorem.
Focus on triangle ABC.
sin(angle) = opposite/hypotenuse
sin(18) = 8/x
x*sin(18) = 8
x = 8/sin(18)
x = 25.888544 approximately
x = 25.9 feet when rounding to the nearest tenth, i.e. one decimal place.