Question

Xochitl 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 7000 feet. Xochitl initially measures an angle of elevation of 19degrees

∘
to the plane at point AA. At some later time, she measures an angle of elevation of 41degrees
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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 AA to point BB, we can use trigonometry and the concept of constant altitude. By finding the height the plane rose and using the tangent function, we can calculate the distance traveled. The distance is approximately 20090 feet.

Step-by-step explanation:

To find the distance the plane traveled from point AA to point BB, we can use the concept of trigonometry and the fact that the plane maintained a constant altitude of 7000 feet.

First, we need to find the height the plane rose from point AA to BB. This can be calculated by taking the difference in the angles of elevation:

41° - 19° = 22°.

To find the height, we can use the tangent function:

tan(22°) = opposite / adjacent.

Since the opposite side is the height and the adjacent side is the distance traveled by the plane, we have:

tan(22°) = height / distance.

Next, we rearrange the equation to solve for the distance:

distance = height / tan(22°).

Plugging in the values, we get:

distance = 7000 / tan(22°) = 20090 feet.

Therefore, the distance the plane traveled from point AA to point BB is approximately 20090 feet.