SOLUTION: Antoinette attaches a wire from the top of an 8-foot pole to the ground. The wire makes an angle of elevation of 45 degrees with the ground. What is the length of the wire?

Question 599589: Antoinette attaches a wire from the top of an 8-foot pole to the ground. The wire makes an angle of elevation of 45 degrees with the ground. What is the length of the wire?
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
Hi, there--
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We will assume the the wire is stretched straight, and the pole forms a right triangle with the ground. Then we have a right triangle, and we can use a trigonometric relationship (sin, cos, or tan) to find the wire length.
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Let w be the length of the wire.
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The angle (45 degrees) formed by the wire and the ground is the angle opposite the pole. The wire is the hypotenuse of the triangle (it's the side across from the right angle formed by the pole and the ground.)
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We have the side opposite and the hypotenuse, so we use the sine relationship:

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The sine of a 45-degree angle is sqrt(2) divided by 2 or about 0.7071.
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The wire is about 11.31 feet long.
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That's it! Feel free to email via gmail if you have questions about the solution.
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Ms.Figgy
math.in.the.vortex@gmail.com

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