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Sarah sights the top of the Statue of Liberty from the ground. If Sarah is 5 feet tall and is standing 166 feet from the base of the statue, and the Statue of Liberty is 300 feet tall, find the angle of elevation.

Sagot :

Using the slope concept, it is found that the angle of elevation is of 60.6º.

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 300 - 5 = 295 feet.
  • The horizontal change is of 166 feet.
  • The angle is of [tex]\alpha[/tex].

Hence:

[tex]\tan{\alpha} = \frac{295}{166}[/tex]

[tex]\tan{\alpha} = 1.77710843373[/tex]

[tex]\tan^{-1}{\tan{\alpha}} = tan^{-1}{1.77710843373}[/tex]

[tex]\alpha = 60.6^\circ[/tex]

The angle of elevation is of 60.6º.

You can learn more about the slope concept at https://brainly.com/question/18090623

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