i put a topic before tf..... anyways its angle of depression, trigonometry

Question

im doing angle of depression and the question says "a man on the bow of a cruise ship, spots a man in the water. he throws a rope that is 50 ft long and he knows the water is 20 feet underneath him. what is the angle of depression that the rope is at. i already drew a picture and and found the angle of elevation but i need help finding the angle of depression

whats taking so long

Answer 1

The angle of elevation between the man in the water to the man on the ship will be the same as the angle of depression from the man on the ship to the man in the water because opposite angles between parallel lines are equal.

From the perspective of the man in the water,

sin(θ) = opp/hyp = 20/50

θ = sin^-1(0.4) = 23.58°

which is also the angle of depression from the man on the bow of the ship to the man in the water.