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Use the cosine law to solve for the unknown side or angle. Round answers to the nearest tenth.

1. 
   
   
   Solution

   \(\begin{align}
    a^2 &= b^2 + c^2 - 2bc\cos A \\
    x^2 &= \left( {43} \right)^2 + \left( {19} \right)^2 - 2\left( {43} \right)\left( {19} \right)\cos 85^\circ  \\
    x^2 &= 2 \thinspace 067.587... \\
    x &= 45.470... \\
    x &\doteq 45.5\thinspace {\rm{ in}} \\
    \end{align}\)
   
   
   
   
   
   
   
   
2. 
   
   
   Solution

   \[\begin{align}
    \cos A &= \frac{{b^2 + c^2 - a^2 }}{{2bc}} \\
    \cos x &= \frac{{\left( {23} \right)^2 + \left( {51} \right)^2 - \left( {72} \right)^2 }}{{2\left( {23} \right)\left( {51} \right)}} \\
    \cos x &= \frac{{ - 2\thinspace 054}}{{2\thinspace 346}} \\
    \cos x &= - 0.875... \\
    x &= \cos ^{ - 1} \left( { - 0.875...} \right) \\
    x &= 151.108...^\circ  \\
    x &\doteq 151.1^\circ  \\
    \end{align}\]