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A tree is 15 feet tall. A wire runs from the top of the tree to a point feet from its base. The wire is √250 long. Estimate the length of the wire to the nearest hundredth of a foot

User Jadero
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Answer:

the length of the wire from the top of the tree to a point 5 feet from its base is approximately 5 feet

Explanation:

To estimate the length of the wire, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the tree forms the vertical side, the distance from the base of the tree to the point where the wire touches the ground forms the horizontal side, and the wire itself is the hypotenuse. Given that the tree is 15 feet tall and the wire is √250 feet long, we can use the Pythagorean theorem to find the length of the horizontal side. Let's call the length of the horizontal side "x". According to the Pythagorean theorem, we have the following equation: 15^2 + x^2 = (√250)^2 Simplifying this equation, we have: 225 + x^2 = 250 Subtracting 225 from both sides, we get: x^2 = 250 - 225 x^2 = 25 Taking the square root of both sides, we find: x = √25 x = 5 Therefore, the length of the wire from the top of the tree to a point 5 feet from its base is approximately 5 feet.

User Romel
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