SOLUTION: A shed is 8 ft wide. One rafter makes an angle of 30 degrees with the horizontal on one side of the roof. A rafter on the other side makes an angle of 70 degrees with the horizonta

Algebra ->  Trigonometry-basics -> SOLUTION: A shed is 8 ft wide. One rafter makes an angle of 30 degrees with the horizontal on one side of the roof. A rafter on the other side makes an angle of 70 degrees with the horizonta      Log On


   

Question 948340: A shed is 8 ft wide. One rafter makes an angle of 30 degrees with the horizontal on one side of the roof. A rafter on the other side makes an angle of 70 degrees with the horizontal. Calculate the length of the shorter raft t the nearest foot. please provide a sketch that what i really need help with. thank you in advance
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
The description is like a triangle with base 8 units and angles at the base of 30 degrees and 70 degrees. Law Of Sines will help to find both of the other sides of this triangle.


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Sum of the angles determines the upper angle's measure:


Equation according to Law Of Sines:
x, the shorter side.

x%2Fsin%2830%29=8%2Fsin%2880%29

highlight%28x=8%28sin%2830%29%2Fsin%2880%29%29%29
Near to x=4.06