SOLUTION: An architextra designs a house that is 12 m wide. The rafters holding up the roof are equal length and meet at an angle of 68 degree. The rafters extend 0.6 m beyond the supporting
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Question 1037266: An architextra designs a house that is 12 m wide. The rafters holding up the roof are equal length and meet at an angle of 68 degree. The rafters extend 0.6 m beyond the supporting wall. How long are the rafters? Answer by Cromlix(4381) (Show Source):
You can put this solution on YOUR website! Hi there,
Consider that the problem
is an isosceles triangle.
Two equal sides (the rafters
from apex to supporting wall.)
If the the top angle = 68 degrees,
then the two side angles each =
(180 - 68)/2 = 56 degrees.
Now label the triangle
A where the 68 degrees are.
B and C on opposing points
of the triangle.
Using Sine Rule
a/SinA = b/sinB = c/Sinc
We will use a/SinA = b/SinB
12/Sin(68) = b/Sin(56)
Cross multiply:
b = 12 x Sin(56)/Sin(68)
b = 10.73 m (2 decimal places)
Rafter = 10.73 + 0.6 = 11.33 m.
Hope this helps :-)
