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

Question

Eileen Summers

Mathematics

9 May, 20:15

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

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Anastasia Stokes · Answer 1

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.