How can we calculate the height of an airplane when the pilot sights an atoll at an angle of depression of 10 degrees, with a horizontal distance of 5172 meters from the airplane to the atoll?

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To find the height of the airplane above the water when the pilot sights the atoll at a 10-degree angle of depression, we can use some basic trigonometry. The angle of depression is the angle formed by the line of sight of the pilot looking down at the atoll and the horizontal line from the pilot. In this case, we have:

  • Angle of depression (θ): 10 degrees
  • Horizontal distance (d): 5172 meters

To find the height (h) of the airplane, we can use the tangent function, which relates the opposite side (height of the airplane) to the adjacent side (horizontal distance) in a right triangle:

tan(θ) = opposite / adjacent

This means:

tan(10 degrees) = h / 5172

To isolate ‘h’, we can rearrange the formula:

h = 5172 * tan(10 degrees)

Now, calculating the height:

h ≈ 5172 * 0.1763 (approximation of tan(10 degrees))

h ≈ 913.77 meters

Thus, the airplane is approximately 913.77 meters above the surface of the Pacific Ocean when the pilot sights the atoll.

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