Question

A lighthouse keeper has a 10 degrees angle of depression between the horizontal light beam and the line of sight from the ship. If the keeper is 19 m above water, how far is the ship from the base of the lighthouse?

Answer 1

107.75m
This is a trigonometric ratio problem. the angle of depression (10) is opposite the height (19m) and the distance is adjacent to the distance (x). opposite ad adjacent sides to the angle is a tangent problem.
$tan \theta = \frac{opp}{adj}$
plus in values, we know.
$tan (10) = \frac{19}{x}$
switch tan(10) and x using the products property.
$x = \frac{19}{tan (10)}$
plug in to calulator to get answer
x=107.75