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20 June, 13:53

A 13 foot ladder leans on a wall. The bottom of the ladder is 5 feet from the wall. If the bottom is pulled out 3 feet farther from the wall, how far does the top of the ladder move down the wall? (Hint: the ladder, wall and the ground form a right triangle.)

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  1. 20 June, 14:14
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    This requires Pythagoras' theorem which says that the square of the hypotenuse = square of another side + the square of another side.

    Therefore, a² = b² + c² where a is the length of the ladder, and b and c are the wall and floor.

    If the ladder is 13 feet long, and the bottom of the ladder is 5 feet long then:

    13² = 5² + c²

    So 13² - 5² = c²

    So c² = 144, and √144 = 12. So c = 12.

    The second part is:

    13² = 8² (because 5 + 3 = 8) + c²

    Therefore, 13² - 8² = c²

    c² = 105

    c = √105 so c = 10.25 (rounded to 2 dp)

    Finally, since c indicates how high the ladder is against the wall, to find the distance moved you need to do 12 - 10.25 so the distance moved is 1.75 feet.
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