A flagpole is 53 feet tall. A rope is tied to the top of the flagpole and secured to the ground 28 feet from the base of the flagpole. What is the length of the rope?

1 Answer
Geoff K.
May 23, 2018

The rope is (approximately) 59.94 feet long.

Explanation:

The given distances are the legs of a right triangle. One leg (the flagpole's height) is 53 feet; the other leg (the distance from the base of the flagpole to the base of the rope) is 28 feet.

We're asked to calculate the hypotenuse of this triangle (the length of the rope).

The most direct way to do this is with the Pythagorean theorem, which says:

For a right triangle with legs #a# and #b# and hypotenuse #c#, we have #a^2+b^2 = c^2.#

Our legs are 53 feet and 28 feet, so we plug these into the formula to get:

#"    "a^2"     "+"    "b^2"     "=c^2#
#("53 ft")^2 + ("28 ft")^2 = c^2#
#"2,809 ft"^2+"784 ft"^2 = c^2#
#"         ""3,593 ft"^2"       " = c^2#

Since we want #c# and not #c^2#, we take the square root of both sides to get:

#sqrt("3,593 ft"^2) = sqrt(c^2)#
#"59.94 ft" ~~ c#

So the length of the rope is (approximately) 59.94 feet.

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