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Space Shuttle Marion is observing the launch of a space
shuttle from the command center. When she first sees the
shuttle, the angle of elevation to it is 16°. Later, the angle
of elevation is 74°. If the command center is 1 mi from the
launch pad, how far did the shuttle travel while Marion was
watching? Round to the nearest tenth of a mile,

Sagot :

Using the slope concept, it is found that the shuttle traveled 3.2 miles while Marion was watching.

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.

Initially, the angle of elevation is of 16º, with an elevation of 1 mi, hence:

[tex]\tan{16^\circ} = \frac{1}{x_1}[/tex]

[tex]x_1 = \frac{1}{\tan{16^\circ}}[/tex]

[tex]x_1 = 3.5[/tex]

Then, at the end, the angle will be of 74º, with the elevation remaining constant, hence:

[tex]\tan{74^\circ} = \frac{1}{x_2}[/tex]

[tex]x_2 = \frac{1}{\tan{74^\circ}}[/tex]

[tex]x_2 = 0.3[/tex]

The distance is:

[tex]d = x_1 - x_2 = 3.5 - 0.3 = 3.2[/tex]

The shuttle traveled 3.2 miles while Marion was watching.

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

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