Question

from the top of a light house, the angles of depression of two ships on the opposite sides of it are observed to be 30 degrees and 60 degrees. If the height of the light house is h metres and the line joining the ships passes through the foot of the light house, show that the distance between the ships is 4h/root 3

Answer 1

Let the top of light house be point A and its base be B. AB= h. Let ship 1 be at point C and 2 be at point D. Distance between ship one and two = BC+BD as both on opposite side of light house. As angle of depression is congruent to angle of elevation, angle CAB will be 60 degree and similarly angle BAD will be 30 degree. Using properties of 30-60-90 Triangle or pythagoras theorem, CB= root 3 h and BD= h/ root 3. CD = BC + BD= root 3 h + h/root 3= 3h +h /root 3 =4h/ root 3.