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Nevaeh 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 7475 feet.
Nevaeh initially measures an angle of elevation of 16° to the plane at point A. At
some later time, she measures an angle of elevation of 43° to the plane at point B.
Find the distance the plane traveled from point A to point B. Round your answer to
the nearest tenth of a foot if necessary.
INTL
0

Sagot :

Using the slope concept, it is found that the distance the plane traveled from point A to point B was of 18052.4 ft.

What is a slope?

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

At point A, the vertical change is of 7475 ft, with an angle of 16º, hence the equation below can be solved to find the position:

[tex]\tan{16^\circ} = \frac{7475}{x_A}[/tex]

[tex]x_A = \frac{7475}{\tan{16^\circ}}[/tex]

[tex]x_A = 26068.4[/tex]

At point B, the angle is of 43º, hence:

[tex]\tan{43^\circ} = \frac{7475}{x_B}[/tex]

[tex]x_B = \frac{7475}{\tan{43^\circ}}[/tex]

[tex]x_B = 8016[/tex]

Hence, the distance in feet is given by:

[tex]d = x_A - x_B = 26068.4 - 8016 = 18052.4[/tex]

More can be learned about the slope concept at https://brainly.com/question/18090623

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