A ladder 9cm long leans against a wall if the foot of the ladder is 4.5cm away the wall how far up the wall does the ladder reach.
9 cm ladder?
Are you sure?
A 3" by 5" file card is almost 9 cm across.
It is a ladder for lame grasshoppers.
height up= sqrt(81-4.5^2) cm=7.79cm
grasshopper also needs wings clipped, 8 cm is not very high.
To find out how far up the wall the ladder reaches, we can use the Pythagorean theorem. According to the theorem, in a right-angled triangle, the square of the length of the hypotenuse (which is the ladder) is equal to the sum of the squares of the other two sides.
Let's consider the ladder as the hypotenuse, the distance between the foot of the ladder and the wall as one side, and the distance we need to find as the other side.
Using the Pythagorean theorem, we have:
(Length of hypotenuse)^2 = (Length of one side)^2 + (Length of other side)^2
Applying the values we know, we have:
(9cm)^2 = (4.5cm)^2 + (Length of other side)^2
Simplifying the equation:
81cm^2 = 20.25cm^2 + (Length of other side)^2
Taking the difference:
(Length of other side)^2 = 81cm^2 - 20.25cm^2
(Length of other side)^2 = 60.75cm^2
Taking the square root of both sides:
Length of other side = √60.75cm^2
Length of other side ≈ 7.8cm
Therefore, the ladder reaches approximately 7.8cm up the wall.
To find out how far up the wall the ladder reaches, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (in this case, the ladder) equals the sum of the squares of the other two sides (in this case, the distance of the foot of the ladder from the wall and the height the ladder reaches on the wall).
Let's define the following variables:
- Length of the ladder (hypotenuse) = 9 cm
- Distance of the foot of the ladder from the wall = 4.5 cm
- Height the ladder reaches on the wall = x cm
Using the Pythagorean theorem, we can set up the equation as follows:
(4.5)^2 + x^2 = 9^2
Simplifying the equation, we have:
20.25 + x^2 = 81
Subtracting 20.25 from both sides, we get:
x^2 = 60.75
Taking the square root of both sides, we find:
x = √60.75
Calculating this, we get:
x ≈ 7.8 cm
Therefore, the ladder reaches approximately 7.8 cm up the wall.