Question

na figura seguinte, calcule as medidas x e y indicadas

Answer 1

Através da trigonometria:

x + y = 9

x√3 = 9

x = 9/√3

x = 9√3/3

x = 3√3

3√3 + y = 9

y = 9 - 3√3

y = 3(3 - √3)

Resposta: x = 3√3 e y = 3(3 - √3)  

Answer 2

Explicação passo-a-passo:

=> Valor de x

$\sf tg~60^{\circ}=\dfrac{cateto~oposto}{cateto~adjacente}$

$\sf \sqrt{3}=\dfrac{9}{x}$

$\sf x\sqrt{3}=9$

$\sf x=\dfrac{9}{\sqrt{3}}$

$\sf x=\dfrac{9}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}$

$\sf x=\dfrac{9\sqrt{3}}{3}$

$\sf \red{x=3\sqrt{3}}$

=> Valor de y

$\sf tg~45^{\circ}=\dfrac{cateto~oposto}{cateto~adjacente}$

$\sf 1=\dfrac{x+y}{9}$

$\sf x+y=9\cdot1$

$\sf x+y=9$

Substituindo $\sf x~por~3\sqrt{3}$:

$\sf 3\sqrt{3}+y=9$

$\sf \red{y=9-3\sqrt{3}}$