Question

Triunghiul ABC are AB = 6 cm, BC = 4 radical din 3 cm și AC = 2 radical din 3 cm (figura 9). Determinaţi măsura unghiului C.

Answer 1

 

$\displaystyle\bf\\Se da:\\\Delta ABC~in~care\\AB = 6~cm\\BC = 4\sqrt{3}~cm\\AC = 2\sqrt{3}~cm\\\\Verificam~daca~\Delta ABC~este~dreptunghic.\\\\AC^2+AB^2=BC^2\\\\6^2+\Big(2\sqrt{3}\Big)^2=\Big(4\sqrt{3}\Big)^2\\\\36+4\times3=16\times3\\\\36+12=48\\48=48~~(adevarat)$

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$\displaystyle\bf\\\implies~~\Delta ABC~este~dreptunghic.\\\implies~~\angle A=90^o\\\implies~~\angle B~si~\angle C~sunt~complementare.\\\\sinB=\frac{c.o.}{ip}=\frac{AC}{BC}=\frac{2\sqrt{3}}{4\sqrt{3}}=\frac{2}{4}=\frac{1}{2}\\\\\implies~\angle B=30^o\\\\\implies~\angle C=90^o-30^o\\\\\boxed{\bf\angle C=60^o}$