Question

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 of the tree to the nearest hundredth?

Answer 1

Answer:
`6.34\ ft`

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)=(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`