A ladder is in a safe position if the height it reaches on the wall is four times the distance of the base from the wall. To the nearest tenth of a foot, find the length of the following ladder. The ladder must reach a 16-foot height.
pythagorean theorem.....if the height is 4 times, and it must reach 16, then the distance along the horizontal must be 4. so 4^2 + 16^2 = c^2. where c is the length of the ladder. Use a calculator to solve.
Idk. Somone post a logical answer.
To find the length of the ladder, we need to use the given information that the height it reaches on the wall is four times the distance of the base from the wall.
Let's assume the distance of the base from the wall is x feet.
According to the given information, the height the ladder reaches on the wall is four times x, which is 4x feet.
Now, we can form the equation:
4x = 16
To solve for x, let's divide both sides of the equation by 4:
4x/4 = 16/4
x = 4
So, the distance of the base from the wall is 4 feet.
To find the length of the ladder, we can use the Pythagorean theorem, which states that in a right-angled triangle (where the ladder is the hypotenuse), the square of the hypotenuse (ladder length) is equal to the sum of the squares of the other two sides.
In this case, the ladder is the hypotenuse, the height on the wall is the opposite side, and the distance of the base from the wall is the adjacent side.
We can use the formula:
ladder length^2 = (base distance)^2 + (height on wall)^2
Substituting the values we have:
ladder length^2 = 4^2 + 16^2
ladder length^2 = 16 + 256
ladder length^2 = 272
To find the length of the ladder, we can take the square root of both sides:
ladder length = √272
Using a calculator, we find:
ladder length ≈ 16.5 feet
Therefore, the length of the ladder, to the nearest tenth of a foot, is 16.5 feet.