500 meters and angle of depression of 40 degrees. determine the submarine depth under water?

If it is 500 metres underwater when measured from a 40 degree angle, you can use trigonometry. 500 metres is the hypotenuse, and the angle from the submarine to the surface of water is 90. It is a right-angled triangle. 
Using sin, where S = O/H, we have no opposite, only angles and a hypotenuse. So, sin 30 (the angle) = O/500. By multiplying each side by 500 to cancel O out, you get sin 30 x 500 = O. 
So, The depth (from a 90 degree angle to the surface) = 294 metres.