Answer:
12068 ft
Explanation:
You want the horizontal distance between two points at an elevation of 6875 ft, if one of them has an angle of elevation of 16°, and the other has an angle of elevation of 30°.
Tangent
The tangent relation is useful for relating legs of a right triangle and one of the acute angles in that triangle. The mnemonic SOH CAH TOA tells you the relation is ...
Tan = Opposite/Adjacent
Here, the side adjacent to the angle of elevation is the horizontal distance to the airplane. The side opposite is the airplane's elevation. This lets us write two distance equations which can be combined to find the distance of interest.
tan(16°) = 6875/A . . . . . . . where A is the ground distance to point A
tan(30°) = 6875/B . . . . . . . where B is the ground distance to point B
Solution
Solving these for the two distances, we have ...
A = 6875/tan(16°)
B = 6875/tan(30°)
Then the distance of interest is ...
A -B = 6875/tan(16°) -6875/tan(30°) ≈ 12068 ft
The distance from point A to point B is about 12,068 feet.