Find the length of the side labeled x. round intermediate values to the nearest tenth. use the rounded values to calculate the next value. round your final answer to the nearest tenth.

1. First, you must calculate the height (h) of the triangle, as below:
 
 Tan(α)=Opposite/Adjacent
 
 α=30º
 Opposite=16
 Adjacent=h
 
 2. When you substitute these values into Tan(α)=Opposite/Adjacent, you obtain:
 
 Tan(α)=Opposite/Adjacent
 Tan(30º)=16/h
 
 3. Now, you must clear "h":
 
 h(Tan(30º))=16
 h=16/Tan(30º)
 h=27.7
 
 4. The value of "x" is:
 
 Cos(β)=Adjacent/Hypotenuse
 
 β=41º
 Adjacent=h=27.7
 Hypotenuse=x
 
 5. When you substitute these values into Cos(β)=Adjacent/Hypotenuse, you have:
 
 Cos(β)=Adjacent/Hypotenuse
 Cos(41º)=27.7/x
 
 6. You must clear "x", as below:
 
 x(Cos(41º))=27.7
 x=27.7/Cos(41º)
 
 7. Therefore, the lenght "x" is:
 
 x=36.70

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