Question

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

Answer 1

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$\sqrt{2}$

Answer 2

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. :)