To calculate the length of the staircase:
\[ SL = \sqrt{(N^2 \cdot T^2) + (N \cdot H^2)} \]
Where:
The staircase length refers to the total distance or the hypotenuse of the staircase from the bottom to the top. This measure is often used in construction to determine the actual length of a staircase based on the number of steps, tread depth, and step height. It helps in understanding the space required for the staircase and ensuring it fits within the design constraints of the building.
Let's assume the following values:
Using the formula:
\[ SL = \sqrt{(10^2 \cdot 11^2) + (10 \cdot 7^2)} = \sqrt{(100 \cdot 121) + (10 \cdot 49)} = \sqrt{12100 + 490} = \sqrt{12590} \approx 112.2 \text{ inches} \]
The length of the staircase is approximately 112.2 inches.
Let's assume the following values:
Using the formula:
\[ SL = \sqrt{(8^2 \cdot 9^2) + (8 \cdot 6^2)} = \sqrt{(64 \cdot 81) + (8 \cdot 36)} = \sqrt{5184 + 288} = \sqrt{5472} \approx 74.0 \text{ inches} \]
The length of the staircase is approximately 74.0 inches.