To calculate the length of the staircase, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (a and b) is equal to the square of the hypotenuse (c). In this case, the height of the staircase is one shorter side, and the slanted height is the hypotenuse, so we can set up the equation:
a^2 + b^2 = c^2
where a = 3.2 m (height), b = unknown (length of staircase), and c = 4.7 m (slanted height).
Solving for b:
b^2 = c^2 - a^2
b^2 = (4.7)^2 - (3.2)^2
b^2 = 22.09
b = sqrt(22.09)
b = 4.7
Therefore, the length of the staircase is approximately 4.7 meters.
Here's a diagram to help visualize the problem: