I've corrected the given from 68.3 to 683meters.
For the illustration please see this (placed on my fb profile)
https://www.facebook.com/photo.php?fbid=3633779889920&set=a.1100830367765.2014805.1436862519&type=1&relevant_count=1&ref=nf
Solution:
(a) Let d = depth of water @ galleon's location
Use sine of angle of depression = opposite / hypotenuse.
sin 27°52′=d/683
d = 683sin 27°52′ ---> Multiply both sides by 683.
d = 319.24 meters --->Ans. depth of water @ galleon's location
(b) Let x = distance the ship would sail to be directly above the galleon
Use cosine of angle of depression = adjacent / hypotenuse.
cos 27°52′=d/683
x = 683cos 27°52′ ---> Multiply both sides by 683.
x = 603.8 meters --->Ans. distance the ship would sail to be directly above the galleon
(b) Let angle B = angle of depression of the galleon when the ship has gone 520 m
Use tangent of angle of depression(angle B) = opposite / adjacent.
tan (angle B) = d/x-520
tan (angle B) = 319.24/(603.8-520) ---> Solved from (a)d=319.24 and (b)x=603.8
(angle B) = arctan (319.24/83.8) ---> Get arctan of both sides.
(angle B) = 75.29° or 75°17′ ---> Ans. angle of depression of the galleon when the ship has gone 520 m
Answers;
(a) depth of water @ galleon's location = 319.24 meters
(b) distance the ship would sail to be directly above the galleon = 603.8 meters
(c) angle of depression of the galleon when the ship has gone 520 m= 75.29° or 75°17′
God bless. Email me- rmnavalta@yahoo.com