Nível I ⇒ Problema 43 - Triângulos -Vol. 2 Tópico resolvido

[petrasMOD]

Calcular [tex3]\alpha ^o [/tex3].
A) 8^o
B) 12^o
C) 15^o
D) 18^o
E) 18^o30'

Resposta

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Resposta: C

[petrasMOD]

[tex3]\mathsf{ ∡FCE=45^∘ \therefore ∡CEF=45^∘\\
∡BED=135^∘: ∡BDE=180^∘−15^∘−135^∘=30^∘\\
AB=AC=x\\
BC=\sqrt x \implies BE=\frac{BC}{2}=\frac{x}{\sqrt2} \\
T.Senos: △BDE:\\
\frac{BD}{sen135^∘} =\frac{BE} {sen30^∘} \implies \frac{BD}{\frac{1}{\sqrt2}} = \frac{ \frac{X}{\sqrt2}}{\frac{1}{2}} \implies BD = x\\
\therefore △ABD_{(isosc.)}\\
∡ABD=30^∘ \therefore ∡BAD=\frac{180^∘−30^∘}{2}=75^∘=90^∘−α→\boxed{α=15^∘}
}
[/tex3]
(Solução:JonhOmielan)