A 1414​-ft ladder leans against a wall at a point 55 feet above the ground. how far is the bottom of the ladder from the​ wall? give an exac

Question

A 1414​-ft ladder leans against a wall at a point 55 feet above the ground. how far is the bottom of the ladder from the​ wall? give an exact​ answer, then approximate the distance to the nearest hundredth of a foot.

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    2021-11-26T00:01:14+00:00

    Assume ladder length is 14 ft and that the top end of the ladder is 5 feet above the ground.

    Find the distance the bottom of the ladder is from the base of the wall.

    Picture a right triangle with hypotenuse 14 feet and that the side opposite the angle is h.  Then sin theta = h / 14, or theta = arcsin 5/14.  theta is

    0.365 radian.  Then the dist. of the bot. of the lad. from the base of the wall is 

    14cos theta = 14cos 0.365 rad = 13.08 feet.  This does not seem reasonable; the ladder would fall if it were already that close to the ground.

    Ensure that y ou have copied this problem accurately from the original.

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