Question

calcule os catetos de um triângulo retângulo cuja hipotenusa mede 7 cm e um dos ângulos mede 60​

Answer 1

$\large\text{ As ~medidas ~dos ~catetos ~ x = \dfrac{7\sqrt{3} }{2} ~cm, ~~y = \dfrac{7}{2} ~cm ~ }$

Seno do ângulo dado:

$Sen ~x = \dfrac{Cateto ~oposto}{Hipotenusa} \\\\\\Sen ~de ~60^o = \dfrac{\sqrt{3} }{2} \\\\\\ \dfrac{\sqrt{3} }{2} = \dfrac{x}{7} \\\\\\2x = 7\sqrt{3} \\\\\\ x = \dfrac{7\sqrt{3} }{2} ~cm$

Cosseno  de 60º

$Cos ~x = \dfrac{Cateto ~adjacente}{Hipotenusa} \\\\\\Cos ~de ~60^o = \dfrac{1 }{2} \\\\\\ \dfrac{1} {2} = \dfrac{y}{7} \\\\\\2y = 7 ~. ~1 \\\\\\ y = \dfrac{7 }{2} ~cm$

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