# 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?

Mar 16, 2017

$20 \sqrt{2}$ $\text{ft}$

#### 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,

$\rightarrow \sin \left({60}^{\circ}\right) = \frac{x}{40}$

Using the unit circle, we can find that

$\rightarrow \frac{\sqrt{2}}{2} = \frac{x}{40}$

$\rightarrow x = \frac{\sqrt{2}}{\cancel{2}} ^ 1 \cdot {\cancel{40}}^{20}$

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

Hope this helps... :)

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