To determine how far up a wall an 11-meter ladder will reach, we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides of a right triangle.
Let's denote the length of the ladder as "c", the distance from the foot of the ladder to the base of the wall as "a", and the height reached by the ladder on the wall as "b".
According to the problem, we have:
c = 11 meters (length of the ladder)
a = 4 meters (distance from the foot of the ladder to the base of the wall)
By substituting these values into the Pythagorean theorem equation, we get:
c^2 = a^2 + b^2
Substituting the given values:
11^2 = 4^2 + b^2
Simplifying:
121 = 16 + b^2
Rearranging the equation:
b^2 = 121 - 16
b^2 = 105
Taking the square root of both sides:
b = √105
The ladder will reach approximately 10.25 meters up the wall.
How far up a wall will an 11-meter ladder reach, if the foot of the ladder is 4 meters away from the base of the wall?
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