When leaned against a vertical structure, a straight ladder can be used safely if its top is no more than 4 above the base of the structure for every foot that the bottom of the ladder is away from the base. How high can a 22-foot ladder safely reach up a vertical structure? Express your answer as a decimal to the nearest tenth.
______feet
h^2 + d^2 = 22^2
h/d = 4 or less
16 d^2 + d^2 = 22^2
17 d^2 = 22^2
d = 5.336
then h is limited to 4 d = 21.3 feet
21.3
To determine how high a 22-foot ladder can safely reach up a vertical structure, we need to use the given condition: the top of the ladder can be no more than 4 feet above the base of the structure for every foot the bottom of the ladder is away from the base.
Let's use the formula:
Height of the ladder = (4/1) * (Distance of the bottom of the ladder from the base)
In this case, the distance of the bottom of the ladder from the base is 22 feet.
Height of the ladder = (4/1) * 22
Height of the ladder = 88 feet
Therefore, a 22-foot ladder can safely reach up to a height of 88 feet on a vertical structure.
To determine how high a 22-foot ladder can safely reach up a vertical structure, we need to apply the given condition: the top of the ladder should be no more than 4 feet above the base for every foot away from the base.
Let's assume that "x" represents the distance of the bottom of the ladder away from the base. According to the condition, we have:
Top of the ladder = 4 * x
Since the 22-foot ladder reaches the top of the structure, we can set up the following equation:
22 = 4 * x
Now we solve for "x":
x = 22 / 4
x = 5.5
Therefore, the bottom of the ladder is 5.5 feet away from the base. To find out how high the ladder can safely reach, we substitute this value back into the equation:
Top of the ladder = 4 * 5.5
Top of the ladder = 22
This tells us that the top of the ladder reaches the same height as the ladder's length, which is 22 feet. So, the maximum height the 22-foot ladder can safely reach up a vertical structure is 22 feet.
Hence, the answer is:
22 feet.