SOLUTION: An architect designs a house that is 12 m wide. The rafters holding up the roof are equal in length and meet at an angle of 70 degrees. The rafters extend 0.3 m beyond the supporti

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: An architect designs a house that is 12 m wide. The rafters holding up the roof are equal in length and meet at an angle of 70 degrees. The rafters extend 0.3 m beyond the supporting wall. How long are the rafters? This question is from textbook

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
An architect designs a house that is 12 m wide. The rafters holding up the roof are equal in length and meet at an angle of 70 degrees. The rafters extend 0.3 m beyond the supporting wall. How long are the rafters?
:
If you draw rough diagram of this, it will help; The roof and the ceiling form
2 back-to-back right triangles
:
It bisects the top angle so the top angle of the right triangle would be 35 degrees.
:
Half the width of 12 m forms the lower side of the triangle: 6 m
:
The rafter (not counting the .3 m overhang) is the hypotenuse, call it h:
:
We can use the sine of 35 degrees to find the hypotenuse: (side opposite/hypot)
:
sin(35) = 6/h
.573576 = 6/h
h = 6/.573576
h = 10.46 + .3 = 10.76 meters is the length of the rafters
:
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