Question

A 40-foot guy wire is attached to a utility pole to provide support for the pole. The wire forms a 60º angle with the ground. How high up the pole is the wire attached? What is the answer in simplest form?

Answer 1

`20sqrt(2)` `"ft"`

Explanation:

Consider the diagram

We need to find the height upto which the guy wire is connected to the pole which is `x`
To find that, we can use a simple trigonometry function

If you know a little trigonometry, you can say that,

`color(brown)(sin(theta)=("Opposite")/("Hypotenuse")`

The opposite side of `60^circ` is `x`. And the hypotenuse is `40`

So,

`rarrsin(60^circ)=x/40`

Using the unit circle, we can find that

`rarrsqrt(2)/2=x/40`

`rarrx=sqrt(2)/cancel2^1*cancel40^20`

`color(green)(rArrx=20sqrt2` `color(green)("ft"`

Hope this helps... :)

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