Question

Calculați lungimea laturii AC a triunghiului ABC,știind că mB=45grade,
mC=30grade și AB=10

Answer 1

 

$\displaystyle\bf\\Se~da:\\\angle B=45^o\\\angle C=30^o\\AB=10~cm\\Se~cere:\\AC=?\\\\\textbf{Aplicamteorema sinusurilor.}\\\\\frac{AB}{sin~C}=\frac{AC}{sin~B}\\\\\frac{10}{sin~30^o}=\frac{AC}{sin~45^o}\\\\AC=\frac{10\times sin~45^o}{sin~30^o}\\\\\\AC=\frac{10\times\dfrac{\sqrt{2}}{2}}{\dfrac{1}{2}}\\\\\\AC=10\times\dfrac{\sqrt{2}}{2}\times\frac{2}{1}\\\\AC=\dfrac{10\sqrt{2}\times2}{2}\\\\\boxed{\bf~AC=10\sqrt{2}~cm}$