Final answer:
To find the depth attained by the Red October submarine after traveling 789 ft at an angle of depression of 15 degrees, we can use trigonometry. The depth can be found using the tangent function, which relates the angle of depression to the depth and horizontal distance. Applying the equation, we determine that the submarine reached a depth of approximately 210.2 ft.
Step-by-step explanation:
To calculate the depth attained by the Red October submarine, we can use trigonometry. The angle of depression is the angle between the horizontal and the line of sight from the submarine to the ocean floor. Since we know the angle of depression is 15 degrees, we can use the tangent function to find the depth.
The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the depth we want to find, and the adjacent side is the horizontal distance traveled by the submarine. Therefore, we can use the equation tan(15) = depth / 789 ft to solve for the depth. Rearranging the equation, we get depth = tan(15) * 789 ft. Calculating this, we find the depth attained by the submarine is approximately 210.2 ft.