Question

DETERMINE O SENO,COSSENO E A TANGENTE DOS ÃNGULOS DE 30° E 60° GRAUS.ULTILIZE UM TRIANGULO EQUILATERO DE LADOS IGUAIS 8 CM

Answer 1

Descobrindo h:

$a^{2}=b^{2}+c^{2}\\8^{2}=4^{2}+h^{2}\\64=16+h^{2}\\h^{2}=48\\h^{2}=4^{2}*3\\\sqrt{h^{2}}=\sqrt{4^{2}}*\sqrt{3}\\h=4\sqrt{3}~cm$
________________________

$sen~x=cateto~oposto/hipotenusa\\sen~60\º=h/8\\sen~60\º=4\sqrt{3}/8\\sen~60\º=\sqrt{3}/2$

$cos~x=cateto~adjacente/hipotenusa\\cos~60\º=4/8\\cos~60\º=1/2$

$tg~x=cateto~oposto/cateto~adjacente\\tg~60\º=4\sqrt{3}/4\\tg~60\º=\sqrt{3}$
________________________

$sen~x=cateto~oposto/hipotenusa\\sen~30\º=4/8\\sen~30\º=1/2\\\\cos~x=cateto~adjacente/hipotenusa\\cos~30\º=4\sqrt{3}/8\\cos~30\º=\sqrt{3}/2\\\\tg~x=cateto~oposto/cateto~adjacente\\tg~30\º=4/(4\sqrt{3})\\tg~30\º=1/\sqrt{3}\\tg~30\º=\sqrt{3}/3$