Question

4. Calcule x ay:
a)
6
x
y
y​

Answer 1

Explicação passo-a-passo:

a)

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

$\sf \dfrac{1}{2}=\dfrac{y}{6}$

$\sf 2y=6\cdot1$

$\sf 2y=6$

$\sf y=\dfrac{6}{2}$

$\sf y=3$

• Semelhança de triângulos

$\sf \dfrac{x}{y}=\dfrac{6+4}{6}$

$\sf \dfrac{x}{3}=\dfrac{10}{6}$

$\sf 6x=3\cdot10$

$\sf 6x=30$

$\sf x=\dfrac{30}{6}$

$\sf x=5$

b)

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

$\sf \dfrac{\sqrt{3}}{2}=\dfrac{x}{6}$

$\sf 2x=6\sqrt{3}$

$\sf x=\dfrac{6\sqrt{3}}{2}$

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

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

$\sf \dfrac{1}{2}=\dfrac{y}{6}$

$\sf 2y=6\cdot1$

$\sf 2y=6$

$\sf y=\dfrac{6}{2}$

$\sf y=3$