If a 23.5 foot ladder is placed against a vertical wall so that it reaches a height of 21 feet, how far away from the base of the wall are the feet of the ladder?(Enter only the number rounded to one decimal with NO units in the answer box)
Question
If a 23.5 foot ladder is placed against a vertical wall so that it reaches a height of 21 feet, how far away from the base of the wall are the feet of the ladder?(Enter only the number rounded to one decimal with NO units in the answer box)
Solution
This problem can be solved using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the ladder acts as the hypotenuse, the height up the wall is one side of the triangle, and the distance from the wall to the base of the ladder is the other side.
We can set up the equation as follows:
(Length of the ladder)^2 = (Height up the wall)^2 + (Distance from the wall)^2
Substituting the given values:
(23.5)^2 = (21)^2 + (Distance from the wall)^2
Solving for the distance from the wall gives:
(Distance from the wall)^2 = (23.5)^2 - (21)^2
(Distance from the wall)^2 = 552.25 - 441
(Distance from the wall)^2 = 111.25
Taking the square root of both sides gives:
Distance from the wall = sqrt(111.25) = 10.5 (rounded to one decimal place)
So, the feet of the ladder are 10.5 feet away from the base of the wall.
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