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A man wants to cut down a tree in his yard. To ensure that the tree doesn't hit anything, he needs to know the height of the tree. He measures his distance from the tree at 11 meters and the angle of elevation to the tree at 61 degrees. What is the height of the tree to the nearest tenth of a meter?

Respuesta :

Answer:

19.8m

Step-by-step explanation:

In the attached diagram:

  • The man's eye level is at point A,
  • The height of the tree is BC.
  • The angle of elevation at A is 61 degrees.
  • The distance of the man at A to the tree BC is 11 meters.

This forms the right triangle ABC.

We want to determine the height labeled h.

Using Trigonometry:

[tex]\tan \theta =\dfrac{BC}{AB}\\ \tan 61^\circ =\dfrac{h}{11}\\h=11 \times \tan 61^\circ\\h=19.8$ m[/tex]

The height of the tree is 19.8 meters to the nearest tenth of a meter.

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