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The city of Franklin, PA, is at an elevation of 293 meters above sea level. The Venango Regional Airport is at the top of a hill just outside of Franklin, at an elevation of 469 meters above sea level. The road from Franklin to the airport rises at an angle of 13°. To the nearest whole number, how long is the road up the hill?

Respuesta :

Using the slope concept, it is found that the road up the hill is 762 meters long.

What is a slope?

The slope is given by the vertical change divided by the horizontal change.

It's also the tangent of the angle of depression.

In this problem:

  • The vertical change is of 469 - 293 = 176 meters.
  • The horizontal change is the length of the road, of x meters.
  • The angle is of 13º.

Hence:

[tex]\tan{(13^\circ)} = \frac{176}{x}[/tex]

[tex]x = \frac{176}{\tan{(13^\circ)}}[/tex]

[tex]x = 762[/tex]

The road up the hill is 762 meters long.

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

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