What is the height of an airplane flying over the Pacific Ocean if it sights an angle of depression of 5 degrees and the horizontal distance to an atoll is 4629 meters?

To find the height of the airplane above the atoll, we can use some basic trigonometry. In this scenario, we form a right triangle where:

• The angle of depression is 5 degrees.
• The horizontal distance to the atoll (adjacent side) is 4629 meters.
• The height of the airplane (opposite side) is what we want to find.

Using the tangent function, which relates the opposite side to the adjacent side, we can express this relationship as:

tan(angle) = opposite / adjacent

Substituting the values into the formula:

tan(5 degrees) = height / 4629 meters

Now, isolating height (opposite side) gives us:

height = tan(5 degrees) * 4629 meters

Using a calculator or trigonometric table, we find:

tan(5 degrees) ≈ 0.0875

Now we can calculate the height:

height = 0.0875 * 4629 meters ≈ 404.37 meters

Therefore, the height of the airplane above the atoll is approximately 404.37 meters.