|This is called a free body diagram. The upper contact point is replaced with a force vector and force vectors are also pencilled in at the bottom.|
Something interesting happens as the person climbs the ladder; the critical coefficient of friction goes up. The downward force stays constant but the horizontal force goes up as the person gets closer to the top.
|2.7:1 is slightly iffy. 3.7:1 is safe. In case you were wondering about the weird numbers, 2.7:1 is 70% and 3.7:1 is 75 degrees.|
The sweet spot for safety is somewhere in the 3:1 and the 4:1 ratio. Ratios are used because most guys on the job site do not have a protractor to measure the angle but are very good at eyeballing ratios or distance in feet.