treasure divers

one of the hardest math question ive ever seen in my life.are you smart enough to answer it?

a diver on the ocean surface notices two pieces of sunken treasure on the ocean floor. in the area whre he is diving, the water is 115 meters deep and the ocean floor is level. the diver measures and finds that one piece of treasure is at an angle of depression of 11 dgrees and the other piece of treasure is at an angle of depression of 36 degrees.

a) how far must the diver dive to reach the closest piece of treasure (to the nearest meter)?
b) once the diver has reached the closest piece of treasure, how far must he swim to reach the other piece of treasure (to the nearest meter)?

This second part of this question is insoluble since we do not know the angle that the lines of sight make to each other when seen from the boat

a) the closer piece of treasure has a angle of depression (i.e. angle of sight line below horizontal) of 36°. The larger the angle of depression, the closer the object is to the observer.

So we have a right angled triangle height 115, and opposite angle 36°. The distance to swim is the hypotenuse h of this triangle
115/h = sin 36°
h = 115/sin 36°
h ~ 195.65 ~ 196m

b) the distance from the boat to the second piece of treasure is, likewise, 115/sin 11° ~ 603m

But, we do not know where the two pieces are relative to each other. If the line of sight to the first piece is due north, and the the second due east, for example, we can get a distance with some more trigonometry. But absent this information, the answer is indeterminate.

If we naively assume that the line of sight to the two pieces of treasure are on the same bearing, then the distance from the first piece to the second piece is:

The distance on the seafloor to a piece of treasure from directly underneath the boat is the adjacent side a of the triangle. 115/a = tan 36° for the first piece.
a = 115/tan 36
We subtract the two distances to find the distance across the seafloor at a depth of 115m that the diver needs to go from the closer piece of treasure to the farther.
115/tan 11° – 115/tan 36
~ 433m

Incidentally, 115m is a very deep dive. The diver would be in an atmospheric diving suit i.e. an armoured suit.

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