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Juanita measures the angle of elevation from the ground to the top of an18-foot-tall tree as 30°. The image is of a tree whose height is 18 ft and its top is making an angle of 30 degrees with the ground. To the nearest tenth of a foot, how far is she from the tree?

Respuesta :

FriendToDino
As shown in the picture below she and the tree are making a 30-60-90 degree triangle. In the diagram, it is shown the bottom is sqrt(3)*x the side, so she is sqrt(3)*18 or 31.1769.
Ver imagen FriendToDino

Answer:

Juanita is standing 31.17 ft far from the tree.

Step-by-step explanation:

Angle of elevation measured by Juanita = [tex]\theta=30^o[/tex]

Height of the tree = 18 ft

Also, an image of that tree whose height is 18 ft and its top is making an angle of 30°.This means length of the image is equal to the distance at which Juanita is standing.

In fig ΔABC

[tex]\frac{AB}{BC}=\tan\theta[/tex]

[tex]\frac{18 ft}{BC}=\tan 30^o=0.5773[/tex] (tan 30° = 0.5773)

BC = 31.17 ft ≈ 31.2 ft

Juanita is standing 31.2 ft far from the tree.

Ver imagen Tringa0

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