Question

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

Answer 1

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. :)

Answer 2

B

Explanation:

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

note sin60° =
`(√(3) )/(2)` and tan60° =
`√(3)`

sin60° =
`(opposite)/(hypotenuse)` =
`(3√(6) )/(y)`

ysin60° = 3
`√(6)`

y ×
`(√(3) )/(2)` = 3
`√(6)`

multiply both sides by 2 and divide by
`√(3)`

y v= 6
`\sqrt{(6)/(3) }` = 6
`√(2)`

tan60° =
`(opposite)/(adjacent)` =
`(3√(6) )/(x)`

xtan60° = 3
`√(6)`

x ×
`√(3)` = 3
`√(6)`

divide both sides by
`√(3)`

x = 3
`\sqrt{(6)/(3) }` = 3
`√(2)`