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A spotlight on the ground shines a beam of light to the top of a tree that is 12 m tall. The beam of light makes an angle of 40° with the ground. What is the distance from the spotlight to the base of the tree, rounded to the nearest meter? 10 m 14 m 16 m 19 m A right triangle. The perpendicular is labeled 12 meters. The angle made between the base and the hypotenuse is labeled 40 degrees. The angle made between the base and the perpendicular is marked as a right angle.

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lublana

Answer:

B.14 m

Step-by-step explanation:

We are given that

Height of tree=12 m

[tex]\theta=40^{\circ}[/tex]

We have to find the distance between the spotlight and the base of tree.

In triangle ABC

AB=12 m

[tex]tan\theta=\frac{perpendicular\;side}{base}[/tex]

Using the formula

[tex]tan 40=\frac{AB}{BC}=\frac{12}{BC}[/tex]

[tex]BC=\frac{12}{tan 40}=14.3\approx 14 m[/tex]

Hence, option B is true.

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Answer:

14m

Step-by-step explanation:

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