Question

Calcule o valor de x e y nós triângulos abaixo : Por favor me ajudem!!!

Answer 1

Explicação passo-a-passo:

a)

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

$\sf 1=\dfrac{x}{20}$

$\sf x=20\cdot1$

$\sf \red{x=20}$

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

$\sf \dfrac{\sqrt{2}}{2}=\dfrac{20}{y}$

$\sf y\sqrt{2}=20\cdot2$

$\sf y\sqrt{2}=40$

$\sf y=\dfrac{40}{\sqrt{2}}$

$\sf y=\dfrac{40}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}$

$\sf y=\dfrac{40\sqrt{2}}{2}$

$\sf \red{y=20\sqrt{2}}$

b)

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

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

$\sf x\cdot1=2\cdot2$

$\sf \red{x=4}$

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

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

$\sf y\sqrt{3}=2\cdot3$

$\sf y\sqrt{3}=6$

$\sf y=\dfrac{6}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}$

$\sf y=\dfrac{6\sqrt{3}}{3}$

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