Question

Use the distances shown in the following figure to determine the depth of the submarine below the surface of the water. Assume that the line segment between the surface ships is directly above the submarine. (Let a = 741, b = 589, and c = 513. Round your answer to the nearest whole number.)

Answer 1

Cos A = (589^2 + 513^2 -  741^2) / 2 x 589 x 513 = 61,009 / 604,314 = 0.1010
A = cos^-1(0.1010) = 84.2 degrees

Let the depth of the submarine be x, then
sin 84.2 = x / c = x / 513
x = 513 sin 84.2 = 510

Therefore, the depth of the submarine is 510.