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Grayson 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
7225 feet. Grayson initially measures an
angle of elevation of 19 to the plane at
point A. At some later time, he measures
an angle of elevation of 39° 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.

Grayson 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 class=

Sagot :

Using the slope concept, it is found that the distance traveled from point A to point B was of 12060.8 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 7225 feet, with an angle of 19º, hence:

[tex]\tan{19^\circ} = \frac{7225}{x_A}[/tex]

[tex]x_A = \frac{7225}{\tan{19^\circ}}[/tex]

[tex]x_A = 20982.9[/tex]

At point B, the vertical change is of 7225 feet, with an angle of 39º, hence:

[tex]\tan{39^\circ} = \frac{7225}{x_B}[/tex]

[tex]x_B = \frac{7225}{\tan{39^\circ}}[/tex]

[tex]x_B = 8922.1[/tex]

The distance in feet is given by:

[tex]d = x_A - x_B = 20982.9 - 8922.1 = 12060.8[/tex]

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

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