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kogti [31]
3 years ago
7

Identify the values of the variables. Give your answers in simplest radical form. HELP ASAP!!

Mathematics
2 answers:
kumpel [21]3 years ago
8 0

Answer:

B

Step-by-step explanation:

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

note sin60° = \frac{\sqrt{3} }{2} and tan60° = \sqrt{3}

sin60° = \frac{opposite}{hypotenuse} = \frac{3\sqrt{6} }{y}

ysin60° = 3\sqrt{6}

y × \frac{\sqrt{3} }{2} = 3\sqrt{6}

multiply both sides by 2 and divide by \sqrt{3}

y v= 6\sqrt{\frac{6}{3} } = 6\sqrt{2}

tan60° = \frac{opposite}{adjacent} = \frac{3\sqrt{6} }{x}

xtan60° = 3\sqrt{6}

x × \sqrt{3} = 3\sqrt{6}

divide both sides by \sqrt{3}

x = 3\sqrt{\frac{6}{3} } = 3\sqrt{2}


MariettaO [177]3 years ago
8 0
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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