Question

calcule x e y, e determine o perímetro de cada figura​

Answer 1

Explicação passo-a-passo:

a)

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

$\sf \dfrac{1}{2}=\dfrac{x}{26}$

$\sf 2x=26\cdot1$

$\sf 2x=26$

$\sf x=\dfrac{26}{2}$

$\sf \red{x=13~cm}$

• $\sf sen~60^{\circ}=\dfrac{cateto~oposto}{hipotenusa}$

$\sf \dfrac{\sqrt{3}}{2}=\dfrac{y}{26}$

$\sf 2y=26\sqrt{3}$

$\sf y=\dfrac{26\sqrt{3}}{2}$

$\sf \red{y=13\sqrt{3}~cm}$

b)

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

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

$\sf x\sqrt{3}=3\cdot16$

$\sf x\sqrt{3}=48$

$\sf x=\dfrac{48}{\sqrt{3}}$

$\sf x=\dfrac{48}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}$

$\sf x=\dfrac{48\sqrt{3}}{3}$

$\sf \red{x=16\sqrt{3}~cm}$

• $\sf sen~30^{\circ}=\dfrac{cateto~oposto}{hipotenusa}$

$\sf \dfrac{1}{2}=\dfrac{16}{y}$

$\sf y\cdot1=16\cdot2$

$\sf \red{y=32~cm}$

c)

• $\sf sen~45^{\circ}=\dfrac{cateto~oposto}{hipotenusa}$

$\sf \dfrac{\sqrt{2}}{2}=\dfrac{x}{22}$

$\sf 2x=22\sqrt{2}$

$\sf x=\dfrac{22\sqrt{2}}{2}$

$\sf \red{x=11\sqrt{2}~cm}$

• $\sf cos~45^{\circ}=\dfrac{cateto~adjacente}{hipotenusa}$

$\sf \dfrac{\sqrt{2}}{2}=\dfrac{y}{22}$

$\sf 2y=22\sqrt{2}$

$\sf y=\dfrac{22\sqrt{2}}{2}$

$\sf \red{y=11\sqrt{2}~cm}$