URGENTEEEEEEEEEE!! TRIGONOMETRIA
Na figura abaixo, h= √2, α= 30º e β= 60º. Calcule a medida x+ y
Tanβ = √3 Tanα = (√3)/3
Tanβ = Y/h
Y = √3 * √2 = √6
Tanα = X/h
X = (√3)/3 * √2
X = √(6)/3
X + Y = (√6)/3 + √6
X + Y = (√24)/3
Calculando x :
[tex]tg30^o=\frac{x}{\sqrt{2}}[/tex]
[tex]x=tg30^o\cdot{\sqrt{2}}[/tex]
[tex]x=\frac{\sqrt{3}}{3}\cdot{\sqrt{2}}[/tex]
[tex]x=\frac{\sqrt{6}}{3}[/tex]
Calculando y :
[tex]tg60^o=\frac{y}{\sqrt{2}}[/tex]
[tex]y=tg60^o\cdot{\sqrt{2}}[/tex]
[tex]y=\sqrt{3}\cdot{\sqrt{2}}[/tex]
[tex]y=\sqrt{6}[/tex]
Calculando x + y :
[tex]\frac{\sqrt{6}}{3}+\sqrt{6}[/tex]
[tex]\boxed{\frac{4\sqrt{6}}{3}}[/tex]
