Question

Item 5 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 PreviousFinish

Answer 1

14 m

Explanation:

We are given that

Height of tree=AB=12 m

`\theta=40^(\circ)`

We have to find the distance from the spotlight to the base of the tree.

We know that

`tan\theta=(perpendicular\;side)/(base)`

`(AB)/(BC)=tan40`

`(12)/(BC)=tan40`

`BC=(12)/(tan40)=14.3\approx 14`

Hence, the distance from the spotlight to the base of the tree=14 m