A1414-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.

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.

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the formula of a slope:

we have the points (-2, 7) and (2, 3). substitute:

answer: the slope is equal -1.