Respuesta :

Answer:

B

Step-by-step explanation:

Since the triangle is right use the sine/ tangent ratios to solve for x and y

note sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] and tan60° = [tex]\sqrt{3}[/tex]

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3\sqrt{6} }{y}[/tex]

ysin60° = 3[tex]\sqrt{6}[/tex]

y × [tex]\frac{\sqrt{3} }{2}[/tex] = 3[tex]\sqrt{6}[/tex]

multiply both sides by 2 and divide by [tex]\sqrt{3}[/tex]

y v= 6[tex]\sqrt{\frac{6}{3} }[/tex] = 6[tex]\sqrt{2}[/tex]

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{3\sqrt{6} }{x}[/tex]

xtan60° = 3[tex]\sqrt{6}[/tex]

x × [tex]\sqrt{3}[/tex] = 3[tex]\sqrt{6}[/tex]

divide both sides by [tex]\sqrt{3}[/tex]

x = 3[tex]\sqrt{\frac{6}{3} }[/tex] = 3[tex]\sqrt{2}[/tex]


bcrawf11
First, put 3(sqrt(6)) in a different form:
sqrt(9) * sqrt(6) = sqrt(54)

We know that a 30 60 90 triangle has a horizontal leg equal to 1, a vertical leg equal to sqrt(3), and a hypotenuse equal to 2.

Find a multiplier/ratio with this information:
(sqrt(54))/(sqrt(3)) = sqrt(18)
given value/accepted value = multiplier

Now, multiply the other values by the multiplier:
1*sqrt(18) = sqrt(18) or 3(sqrt(2))
2*sqrt(18) = 2(sqrt(18)) or 6(sqrt(2))

Your answer would be:
x = 3(sqrt(2))
y = 6(sqrt(2))
Or option b.

If you don’t understand any part of my work, please feel free to comment with a question on this answer. :)

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