Question

Encontre os valores desconhecidos em cada item:

Answer 1

Explicação passo-a-passo:

a)

Seja z a hipotenusa do triângulo ABC

$\sf cos~60^{\circ}=\dfrac{cateto~adjacente}{hipotenusa}$

$\sf \dfrac{1}{2}=\dfrac{4}{z}$

$\sf z\cdot1=2\cdot4$

$\sf z=8$

=> Valor de x

$\sf tg~30^{\circ}=\dfrac{cateto~oposto}{cateto~adjacente}$

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

$\sf \dfrac{\sqrt{3}}{3}=\dfrac{x}{8}$

$\sf 3x=8\sqrt{3}$

$\sf \red{x=\dfrac{8\sqrt{3}}{3}}$

=> Valor de y

$\sf cos~30^{\circ}=\dfrac{cateto~adjacente}{hipotenusa}$

$\sf \dfrac{\sqrt{3}}{2}=\dfrac{z}{y}$

$\sf \dfrac{\sqrt{3}}{2}=\dfrac{8}{y}$

$\sf y\sqrt{3}=2\cdot8$

$\sf y\sqrt{3}=16$

$\sf y=\dfrac{16}{\sqrt{3}}$

$\sf y=\dfrac{16}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}$

$\sf \red{y=\dfrac{16\sqrt{3}}{3}}$

b)

=> Valor de x

Pelo Teorema de Pitágoras:

$\sf x^2=1^2+1^2$

$\sf x^2=1+2$

$\sf x^2=2$

$\sf \red{x=\sqrt{2}}$

=> Valor de y

Pelo Teorema de Pitágoras:

$\sf y^2=x^2+1^2$

$\sf y^2=(\sqrt{2})^2+1^2$

$\sf y^2=2+1$

$\sf y^2=3$

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

=> Valor de z

Pelo Teorema de Pitágoras:

$\sf z^2=y^2+1^2$

$\sf z^2=(\sqrt{3})^2+1^2$

$\sf z^2=3+1$

$\sf z^2=4$

$\sf z=\sqrt{4}$

$\sf \red{z=2}$

=> Valor de w

Pelo Teorema de Pitágoras:

$\sf w^2=z^2+1^2$

$\sf w^2=2^2+1^2$

$\sf w^2=4+1$

$\sf w^2=5$

$\sf \red{w=\sqrt{5}}$