Question

The length of each rafter for a roof is 60 m including a 1 m overhang. The peak is 20.5 m above the horizontal beam. Find the width of the horizontal beam?

Answer 1

The width of the horizontal beam is 110.648... meters.

Step-by-step 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......

`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= √(3060.75)=55.324...`

So, CE = 2× CD = 2× 55.324.... =110.648....

Thus the width of the horizontal beam is 110.648... meters.