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Travis spies an owl in a tall tree. He estimates the height of the tree to be 85 feet and the angle of elevation to the bird from where he stands to be 68°. The leaves on the tree make it difficult for Travis to watch the bird, so he takes several steps away from the tree to get a better view. He now estimates his angle of elevation to be 41°.

How many feet did Travis step back to gain a better view of the bird? Round your answer to the nearest hundredth of a foot.

Respuesta :

Using the slope concept, it is found that he stepped back 63.44 feet.

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.

Initially, we have that:

  • The vertical change is of 85 feet.
  • The horizontal change is his distance d.
  • The angle is of 68º.

Hence:

[tex]\tan{68^{\circ}} = \frac{85}{d}[/tex]

[tex]d = \frac{85}{\tan{68^{\circ}}}[/tex]

[tex]d = 34.34[/tex]

When he stepped back, the angle was of 41º, hence:

[tex]\tan{41^{\circ}} = \frac{85}{d}[/tex]

[tex]d = \frac{85}{\tan{41^{\circ}}}[/tex]

[tex]d = 97.78[/tex]

97.78 - 34.34 = 63.44.

Hence he stepped back 63.44 feet.

You can learn more about the slope concept at https://brainly.com/question/26291396

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