A 15ft. wire is tied to the top of a tree to provide support. If the wire forms a 25° angle with the ground, what is the height

Question

3 years ago

12

of the tree to the nearest hundredth?

1 answer:

lana [24] · Answer 1 · 2022-10-07T00:41:37+03:00

lana [24]3 years ago

4 0

Answer: $6.34\ ft$

Step-by-step explanation:

Given

The length of the wire is $l=15\ ft$

The Wire makes an angle of $25^{\circ}$ with horizontal

Suppose the height of the tree is h

From the figure, we can write

$\Rightarrow \sin 25^{\circ}=\dfrac{h}{l}\\\\\Rightarrow h=l\sin 25^{\circ}\\\Rightarrow h=15\sin 25^{\circ}\\\Rightarrow h=6.34\ ft$

Thus, the height of the tree is $6.34\ ft$