Question

Kayla spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. the plane maintains a constant altitude of 6875 feet. kayla initially measures an angle of elevation of 16degrees ∘ to the plane at point aa. at some later time, she measures an angle of elevation of 30degrees ∘ to the plane at point bb. find the distance the plane traveled from point aa to point bb. round your answer to the nearest foot if necessary.\

Answer 1

To find the distance the plane traveled from point A to B, use the tangent of the given angles and the constant altitude to calculate the horizontal distances at points A and B, then subtract these to get the distance traveled, and round to the nearest foot.

The question involves finding the distance a plane traveled from point A to point B, given the angles of elevation at two points and a constant altitude. We can solve this problem using trigonometry by considering two right-angled triangles formed by the altitude and the line of sight from Kayla to the plane at points A and B.

To find the distance between points A and B (let's call it d), we first need to find the horizontal distances from Kayla to the plane at points A and B (let's call them hA and hB respectively) using the tangent function. The altitude of the plane is constant at 6875 feet.

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After calculating hA and hB, the distance d that the airplane has traveled from A to B is:

d = hB - hA

Finally, round the answer to the nearest foot as necessary.