An observer 80 ft above the surface of the water measures an angle of depression of 0.7° to a distant ship. How many miles is the ship from the base of the lighthouse? (5,280 ft = 1 mile)
+23246 After drawing the picture, note that the complementary angle (at the point 80 ft above the surface of the water) is 89.3°.
Let x represent the distance from the ship to the point on the water directly below the observer.
In the right triangle from the ship to the point on the water directly below the observer to the observer:
tan(89.3°) = x / 80 ---> x = 80·tan(89.3°)
Take this answer, which is in feet, and convert it to miles.
