To find the length of the ladder, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's denote:
- \( h \) as the height of the wall (2.5m)
- \( d \) as the distance from the base of the wall to the base of the ladder (70cm = 0.7m)
- \( L \) as the length of the ladder (what we want to find)
According to the Pythagorean theorem:
\[ L^2 = h^2 + d^2 \]
Substituting the given values:
\[ L^2 = (2.5m)^2 + (0.7m)^2 \]
\[ L^2 = 6.25m^2 + 0.49m^2 \]
\[ L^2 = 6.74m^2 \]
Taking the square root of both sides to solve for \( L \):
\[ L = \sqrt{6.74m^2} \]
\[ L \approx 2.6m \]
So, the length of the ladder is approximately 2.6 meters.
