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

Question

3 years ago

11

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

Mathematics

1 answer:

Troyanec [42] · Answer 1 · 2022-04-19T12:48:32+03:00

Troyanec [42]3 years ago

3 0

Answer:

14 m

Step-by-step 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

$tan\theta=\frac{perpendicular\;side}{base}$

$\frac{AB}{BC}=tan40$

$\frac{12}{BC}=tan40$

$BC=\frac{12}{tan40}=14.3\approx 14$

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