The width of the horizontal beam is 110.648... meters.
Explanation
According to the below diagram, length of each rafter for a roof is AB which is 60 meter, including the over hanged part (BC) of 1 meter.
So, AC= AB - BC = (60-1) meter = 59 meter.
The peak(point A) is 20.5 m above the horizontal beam (CE). That means, AD = 20.5 meter
Now, in right angle triangle ADC, using Pythagorean theorem......
[tex]AC^2= AD^2+ CD^2\\ \\ (59)^2= (20.5)^2+CD^2\\ \\ CD^2= (59)^2 - (20.5)^2 \\ \\ CD^2 = 3060.75\\ \\ CD= \sqrt{3060.75}=55.324...[/tex]
So, CE = 2× CD = 2× 55.324.... =110.648....
Thus the width of the horizontal beam is 110.648... meters.
