Answer:
x = [tex]2\sqrt{3}[/tex] , y = [tex]4\sqrt{3}[/tex] ⇒ A
Step-by-step explanation:
In the 30°-60°-90° triangle, there is a ratio between its three sides
- The length of the side opposite to the angle of measure 30° is half the length of the hypotenuse
- The length of the side opposite to the angle of measure 60° is half the length of the hypotenuse times [tex]\sqrt{3}[/tex]
→ 30° : 60° : 90°
→ 1 : [tex]\sqrt{3}[/tex] : 2
In the given figure
∵ The length of the hypotenuse is y
∵ The length of the side opposite to the angle of measure 30° is x
∵ The length of the side opposite to the angle of measure 60° is 6
→ By using the ratio above
→ 30° : 60° : 90°
→ 1 : [tex]\sqrt{3}[/tex] : 2
→ x : 6 : y
→ By using cross multiplication
∵ x × [tex]\sqrt{3}[/tex] = 1 × 6
∴ x [tex]\sqrt{3}[/tex] = 6
→ Divide both sides by [tex]\sqrt{3}[/tex]
∴ x = [tex]\frac{6}{\sqrt{3}}[/tex]
→ Simplify it by multiplying up and down by [tex]\sqrt{3}[/tex]
∴ x = [tex]\frac{6\sqrt{3}}{3}=2\sqrt{3}[/tex]
∴ x = [tex]2\sqrt{3}[/tex]
∵ y × [tex]\sqrt{3}[/tex] = 6 × 2
∴ y [tex]\sqrt{3}[/tex] = 12
→ Divide both sides by [tex]\sqrt{3}[/tex]
∴ y = [tex]\frac{12}{\sqrt{3}}[/tex]
→ Simplify it by multiplying up and down by [tex]\sqrt{3}[/tex]
∴ y = [tex]\frac{12\sqrt{3}}{3}=4\sqrt{3}[/tex]
∴ y = [tex]4\sqrt{3}[/tex]
