Question

URGENTEEEEEEEEEE!! TRIGONOMETRIA

 

Na figura abaixo, h= √2, α= 30º e β= 60º. Calcule a medida x+ y

Answer 1

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

Answer 2

Calculando x :

 

$tg30^o=\frac{x}{\sqrt{2}}$

 

$x=tg30^o\cdot{\sqrt{2}}$

 

$x=\frac{\sqrt{3}}{3}\cdot{\sqrt{2}}$

 

$x=\frac{\sqrt{6}}{3}$

 

Calculando y :

 

$tg60^o=\frac{y}{\sqrt{2}}$

 

$y=tg60^o\cdot{\sqrt{2}}$

 

$y=\sqrt{3}\cdot{\sqrt{2}}$

 

$y=\sqrt{6}$

 

Calculando x + y :

 

$\frac{\sqrt{6}}{3}+\sqrt{6}$

 

$\boxed{\frac{4\sqrt{6}}{3}}$