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pls answer! Dylan 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 6400 feet.
Dylan initially measures an angle of elevation of 16° to the plane at point A. At some
later time, he measures an angle of elevation of 36° to the plane at point B. Find the
distance the plane traveled from point A to point B. Round your answer to the
nearest foot if necessary.

Answer :

Answer:

13510 ft

Step-by-step explanation:

I have attached a triangle diagram to depict this situation.

From the diagram, we see that distance between A and B is denoted by x.

Now, from trigonometric ratios in this type of triangle, let's first find y.

6400/y = tan 36

y = 6400/tan 36

y = 8808.84 ft

Now, we can find x from;

6400/(8808.84 + x) = tan 16

6400/tan 16 = 8808.84 + x

22319.452 = 8808.84 + x

x = 22319.452 - 8808.84

x ≈ 13510 ft

View image AFOKE88

The distance the plane traveled from point A to point B is 13510 ft

Calculation of the distance:

Here we assume the distance between A and B should be x.

Now the y value should be

[tex]6400\div y = tan 36\\\\y = 6400\div tan 36[/tex]

y = 8808.84 ft

Now, we can find x

[tex]6400\div (8808.84 + x) = tan\ 16\\\\6400\div tan\ 16 = 8808.84 + x[/tex]

22319.452 = 8808.84 + x

x = 22319.452 - 8808.84

x ≈ 13510 ft

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