Answer:
Step-by-step explanation:
It is given that 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., therefore from the figure drawn, we have
AB=12 m and ∠C=40°.
Using the trigonometry in ΔABC, we have
[tex]\frac{AB}{BC}=tan40^{\circ}[/tex]
[tex]\frac{12}{BC}=tan40^{\circ}[/tex]
[tex]\frac{12}{BC}=0.839[/tex]
[tex]BC=\frac{12}{0.839}[/tex]
[tex]BC=14m[/tex]
Thus, the distance from the spotlight to the base of the tree is BC=14 m.
