Extension Ladder Height Calculator

Extension Ladder Height Formula:

\[ Height = Length \times \cos(\theta) \]

Extension Height:

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1. What is the Extension Ladder Height Formula?

The Extension Ladder Height formula calculates the vertical height reached by an extension ladder based on its length and the angle at which it's positioned. This calculation is essential for ladder safety and proper placement.

2. How Does the Calculator Work?

The calculator uses the trigonometric formula:

\[ Height = Length \times \cos(\theta) \]

Where:

\( Length \) — Total length of the extension ladder (ft)
\( \theta \) — Angle between the ladder and the ground (degrees)
\( Height \) — Vertical extension height reached (ft)

Explanation: The cosine function calculates the vertical component of the ladder's length based on the angle of placement.

3. Importance of Proper Ladder Height Calculation

Details: Accurate height calculation ensures ladder safety, prevents overreaching, maintains proper angle (typically 75° for optimal safety), and helps determine if a ladder is appropriate for a specific task.

4. Using the Calculator

Tips: Enter the ladder length in feet and the angle in degrees (typically between 65°-80° for safe use). All values must be valid (length > 0, angle between 0°-90°).

5. Frequently Asked Questions (FAQ)

Q1: What is the ideal ladder angle for safety?
A: The recommended safe angle is approximately 75° (1:4 ratio - for every 4 feet of height, the base should be 1 foot away from the wall).

Q2: Why is the cosine function used?
A: Cosine calculates the adjacent side (vertical height) in a right triangle where the hypotenuse is the ladder length and the angle is between ladder and ground.

Q3: Does this account for ladder overlap?
A: This calculation assumes the full extended length. For extension ladders, remember to account for the overlap section which reduces the effective working length.

Q4: What about ladder weight capacity?
A: This calculator only determines reach height. Always check the ladder's weight capacity and duty rating before use.

Q5: Should I include my reach height?
A: This calculates the ladder's reach height. For working height, add your arm's reach (typically 3-4 feet) while maintaining safe posture on the ladder.