Question

A person in a 300 foot tall lighthouse is attempting to locate a boat floating in the water 720 feet from the bottom of the lighthouse. At what angle of depression should the light be shown to locate the boat?

Answer 1

Answer:

Step-by-step explanation:

Because the line of sight from the top of the lighthouse is parallel to the water, the angle of depression (which is OUTSIDE the right triangle) is alternate interior with the angle of elevation, which is the base angle INSIDE the right triangle this creates.  The base angle that is NOT the right angle, of course.  Because these angles are alternate interior of a transversal cutting a pair of parallel lines, they are congruent.  Therefore, we need to find the measure of the base angle using the 2 sides given.  The height of the lighthouse is the height of the triangle and the distance the boat is from the base of the lighthouse is the side adjacent to the angle.  We are looking at the tangent ratio which is side opposite/side adjacent.  When you need to find a missing angle on your calculator, you willl use the 2nd button and then whichever trig identity you need.  Because we need tangent, we will hit 2nd then tan and get this on our screen:

$tan^{-1}($

Inside that parenthesis, enter 300/720 and hit enter to get your angle.  2 things here:  make sure you are in degrees in your calculator by hitting mode and checking that "degrees" is highlighted instead of radians, and secondly, you do not have to close the parenthesis to get the correct answer.  Your angle measure should be 22.619 degrees, by the way.