Question

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?

Answer 1

14m. I Just took the test and got the question right.

Answer 2

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

`(AB)/(BC)=tan40^(\circ)`

`(12)/(BC)=tan40^(\circ)`

`(12)/(BC)=0.839`

`BC=(12)/(0.839)`

`BC=14m`

Thus, the distance from the spotlight to the base of the tree is BC=14 m.