A 62 foot rope hangs from the top of a pole. When pulled taut to its fullest length the rope reaches a point on the ground 31 feet from the base of the pole. Find the height of the pole to the nearest tenth of a foot. Let p equal the height of the pole.
a^2 + b^2 = c^2
31^2 + p^2 = 62^2
961 + p^2 = 3844
p^2 = 3844 - 961
p^2 = 2,883
p = 53.226 = 53.2
Thank you, Ms. Sue....I had the right concept but was stuck in the last part...
Allie
You're welcome, Allie.
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To find the height of the pole, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the rope acts as the hypotenuse, the height of the pole acts as one side, and the distance from the base of the pole to the point on the ground where the rope reaches is the other side.
Let's set up the equation:
p^2 + 31^2 = 62^2
Simplifying:
p^2 + 961 = 3844
Subtracting 961 from both sides:
p^2 = 2883
Now, to find p, we take the square root of both sides:
p ≈ √2883
Using a calculator, we find that p is approximately 53.7 feet.
Therefore, the height of the pole is approximately 53.7 feet to the nearest tenth of a foot.