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?

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1 Answer
Mar 16, 2017

#20sqrt(2)# #"ft"#

Explanation:

Consider the diagram

enter image source here
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... :)

If you have any doubts, you can ask me at the commennts section.