An airplane over the Pacific Ocean sights an atoll at an 7° angle of depression. If the plane is 850 m above the water, how many kilometers is it from a point 850 m directly above the atoll?
To solve this problem, we can use trigonometric ratios. We know that the angle of depression is 7° and the height of the plane above the water is 850 m. We want to find the distance from the plane to the point directly above the atoll.
Let's call the distance we are trying to find "x" (in kilometers). We can use the tangent function to relate the angle of depression to the height and distance:
tan(angle of depression) = opposite/adjacent
In this case, the opposite side is the height of the plane above the water (850 meters) and the adjacent side is the distance we are trying to find (x kilometers).
So, we can set up the equation:
tan(7°) = 850 / x
To find x, we can rearrange the equation:
x = 850 / tan(7°)
Now, we can calculate the value of x:
x = 850 / tan(7°)
x ≈ 850 / 0.122
x ≈ 6967.2
Therefore, the distance from the point directly above the atoll to the plane is approximately 6967.2 kilometers.
Draw a diagram. You will see that
x/850 = cot 7°
Now solve for x
Don't forget that x is in meters, so divide by 1000 to answer in km.