Question

Aguy wire for a tree is 20 ft. long, making a 21oangle with the ground. How far is the base of the tree from a stake anchoring the wire?

Answer 1

The base of the tree from a stake anchoring the wire is 18.67 feet far.

Explanation:

Given:

the length of the wire = 20 feet

Angle that the wire makes with the ground = 21 degrees

To Find:

The Distance from the base of the tree from the stake anchoring wire = ?

Solution:

We we construct a figure using the given data we end up with the right triangle as shown below

So now we can use the cosine ratio to find the distance from the base of the tree to the anchoring wire

Let d be the distance of base of the tree from a stake anchoring the wire

`Cos(angle) =\frac{\text{Adjacent side}}{Hypotenuse}`

On substituting the values we get

`cos(21^(\circ)) =(d)/(20)`

`d = cos(21^(\circ)) * 20`

d =
`0.9335 * 20`

d = 18.67 feet