Question

An airplane over the Pacific Ocean sights an atoll at an 7° angle of depression. If the plane is 663 m above the water, how many kilometers is it from a point 663 m directly above the atoll?

Answer 1

If the plane is 663 m over the water, then it is 0.663 km over the water, since 1000 m = 1 km. Using that fact, and the tangent function of 7° (tan A = opposite side / adjacent side), where, in this case, the opposite side is the height of the point directly over the atoll, and the adjacent side, x, is the plane's distance to that point (draw a diagram depicting the problem), we get these calculations:

tan 7° = 0.123 = 0.663 km / x ---> x = 0.663 km / 0.123 = 5.390 km, which we can round to 5.4 km.

So the correct answer here is 5.4 km.

Answer 2

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