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Answer :
The length of the caple is √3125 cm. (option C)
What is the length of the caple?
The caple and the tower would form a right triangle. The caple would be the hypotenuse. The tower would be the length and the distance from the base of the tower would be the base.
In order to determine the length of the caple, Pythagoras theorem would be used.
The Pythagoras theorem: a² + b² = c²
where:
- a = length
- b = base
- c = hypotenuse
c² = 25² + 50 ²
c² = 625 + 2500
c² = 3125
c= √3125 cm
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Final answer:
The length of the cable is 25√5 cm.
Explanation:
To find the length of the cable, we can use the Pythagorean theorem. The height of the tower is one side of a right triangle, and the distance from the base of the tower to the point where the cable is stretched is the other side. We can find the length of the cable by finding the hypotenuse.
Using the Pythagorean theorem formula, [tex]a^2 + b^2 = c^2[/tex], where a and b are the lengths of the two sides and c is the length of the hypotenuse, we can substitute the values we know: [tex]25^2 + 50^2 = c^2.[/tex]
Simplifying the equation, we get [tex]625 + 2500 = c^2.[/tex] Adding the values gives us [tex]3125 = c^2.[/tex]Taking the square root of both sides, we find that c = 25√5. Therefore, the length of the cable is 25√5 cm.
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