SOLUTION: A construction company i mass-producing picnic pavilions for national parks. The rafter ends are to be sawed in such a way that they will be vertical when in place. The front is

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A construction company i mass-producing picnic pavilions for national parks. The rafter ends are to be sawed in such a way that they will be vertical when in place. The front is       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 41531: A construction company i mass-producing picnic pavilions for national parks. The rafter ends are to be sawed in such a way that they will be vertical when in place. The front is 8 feet high and the back is 6.5 feet high, and the distance between the front and back is 8 feet. At what angle should the rafters be cut?
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
The shape of the rafter is as below.



AD is back side, BC is front side and AB is the distance between the front and back sides.
So AD = 6.5 ft,BC = 8 ft and AB = 8 ft.
Hence, the required angle is 10.62 degrees
Draw a straight line from D parallel to AB which meets BC at E.
As Hence, BE = AD = 6.5 ft.
So, CE = BC - BE = 8 - 6.5 = 1.5 ft.
Also, DE = AB = 8 ft.
Now, in right angled triangle DEC, let tan%28x%29+=+CE%2FDE
= 1.5%2F8
= 3%2F16
Therefore, x = tan inverse (3/16) = 10.62 degrees