Analyze the diagram below and complete the instructions that follow.

Find the value of x and the value of y.
A. X= 23.y=413
B. 1 = 3, y = 613
C. = 6/3, y = 12
D. x= 23, y = 6

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

→  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]

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