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Answer:
7.28 miles
Step-by-step explanation:
Suppose the distance at closest approach is represented by x. Then the distance to the point of closest approach at the first sighting is ...
d1 = x·tan(62°)
At the second sighting, the distance to the point of closest approach is ...
d2 = x·tan(38°)
The difference of these distances is 8 miles, so we have ...
d1 -d2 = 8 = x(tan(62°) -tan(38°))
Dividing by the coefficient of x, we find ...
x = 8/(tan(62°) -tan(38°)) ≈ 7.2764 . . . . miles
The point of closest approach is about 7.28 miles from the landmark.
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