Para determinar el valor de "c" utilizaremos la Ley de los cosenos(Ver imagen).
Nuestros datos son:
[tex]\begin{array}{ccccccccccccc}\boldsymbol{\bigcirc \kern-8pt \triangleright} \:\:\:\:\sf{a = 25 }&&&&&&\boldsymbol{\bigcirc \kern-8pt \triangleright} \:\:\:\:\sf{b = 15 }&&&&&&\boldsymbol{\bigcirc \kern-8pt \triangleright} \:\:\:\:\sf{\theta = 65}\end{array}[/tex]
Reemplazamos en la fórmula
[tex]\begin{array}{c}\\\sf{c^2 = a^2 + b^2 - 2\cdot a \cdot b\cdot \cos(\theta)}\\\\\sf{c^2 = 25^2 + 15^2 - 2(25)(15)\cdot \cos(65^{\circ})}\\\\\sf{c^2 = 625 + 225-750\cos(65^{\circ})}\\\\\sf{c = \sqrt{625 + 225-750\cos(65^{\circ})}}\\\\\boxed{\boxed{\red{\boldsymbol{\sf{c\approx 23.087}}}}}\end{array}[/tex]
Rpta. La longitud [tex]\overline{AB}[/tex] del triángulo es aproximadamente 23.087 unidades.
[tex]\boxed{\sf{{R}}\quad\raisebox{10pt}{$\sf{\red{O}}$}\!\!\!\!\raisebox{-10pt}{$\sf{\red{O}}$}\quad\raisebox{15pt}{$\sf{{G}}$}\!\!\!\!\raisebox{-15pt}{$\sf{{G}}$}\quad\raisebox{15pt}{$\sf{\red{H}}$}\!\!\!\!\raisebox{-15pt}{$\sf{\red{H}}$}\quad\raisebox{10pt}{$\sf{{E}}$}\!\!\!\!\raisebox{-10pt}{$\sf{{E}}$}\quad\sf{\red{R}}}\hspace{-64.5pt}\rule{10pt}{.2ex}\:\rule{3pt}{1ex}\rule{3pt}{1.5ex}\rule{3pt}{2ex}\rule{3pt}{1.5ex}\rule{3pt}{1ex}\:\rule{10pt}{.2ex}[/tex]
