Question 124733: if a tent pole is 2m high and the rope is 2.4m, then hoe far from the base of the pole should the rope be pegged
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! This problem involves a right triangle.
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Presumably the tent pole is to be vertical and that means that it will be perpendicular
to the ground ... or at an angle of 90 degrees with the ground.
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The rope is fastened to the top of the tent pole and then is stretched out and tied to a
tent peg that is driven in the ground some distance from the base of the tent pole.
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Therefore, the rope forms the long side or hypotenuse of the right triangle. The length of
the tent pole is one of the legs of the triangle, and the distance you are looking for is the
length of the other leg of the triangle.
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You could solve this problem using trigonometry, or you could use the Pythagorean
theorem. Since students normally learn the Pythagorean theorem first, let's use that method
of solving the problem.
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The Pythagorean theorem says that in a right triangle the sum of the squares of the lengths of
the two legs is equal to the square of the hypotenuse. If the lengths of the two legs are
A and B and the length of the hypotenuse is C, then in equation form the Pythagorean
theorem tells you that:
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A^2 + B^2 = C^2
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You know that the length of one of the legs (the tent pole) is 2 meters. Substitute this
length for one of the legs in the equation (say for leg B) and you have:
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A^2 + 2^2 = C^2
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And you know that the hypotenuse (the length of the rope) is 2.4 meters. Substitute this
value for C and the equation then becomes:
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A^2 + 2^2 = (2.4)^2
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Square the two numbers and the equation then is:
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A^2 + 4 = 5.76
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Get rid of the 4 on the left side by subtracting 4 from both sides and you have:
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A^2 = 1.76
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Finally, solve for A by taking the square root of both sides to get:
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A = sqrt(1.76) = 1.326649916 meters
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Round this answer off to A = 1.33 meters
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This tells you that the tent peg should be located at a distance of 1.33 meters from the base
of the tent pole.
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This, of course, does not take into account the amount of rope that is used in tying the
rope to the peg and to the top of the pole. It is based on the assumption that the 2.4 meter
length of the rope is just the length between the peg and the pole.
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Hope this helps you to understand how the problem can be set up and solved.
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