Ladder Problem: Applying Pythagorean Theorem

This problem involves a right-angled triangle formed by the ladder, the wall, and the ground. We can use the Pythagorean theorem to find the unknown horizontal distance.

• Let the length of the ladder be the hypotenuse, $L = 2\text{ m}$.
• Let the height of the wall be one leg, $H = 1.75\text{ m}$.
• Let the horizontal distance from the wall be the other leg, $D$.

Calculating Horizontal Distance

According to the Pythagorean theorem: $D^2 + H^2 = L^2$

We need to find $D$. Rearranging the formula:

$D^2 = L^2 - H^2$

Substitute the given values:

$D^2 = (2)^2 - (1.75)^2$

$D^2 = 4 - 3.0625$

$D^2 = 0.9375$

Now, take the square root to find $D$:

$D = \sqrt{0.9375}$

Determining the Correct Option

We need to estimate the value of $\sqrt{0.9375}$.

• We know that $\sqrt{1} = 1$.
• Since $0.9375$ is less than $1$, its square root must also be less than $1$.
• Calculating the value gives $D \approx 0.9682\text{ m}$.

Therefore, the largest possible horizontal distance $D$ is approximately $0.9682\text{ m}$, which is slightly less than $1\text{ m}$.

The correct option is the one describing a distance slightly less than $1\text{ m}$.