Find the value of each variable. If your answer is not an integer, write it in simplest radical
form with the denominator rationalized.

x = 39/√2

y = (13/2)*√3

Step-by-step explanation:

First let's write the only relation we need here:

Cos(θ) = (adjacent cathetus)/(hypotenuse)

or we also could use:

Sin(θ) = (opposite cathetus)/(hypotenuse).

For this problem, we know that the hypotenuse is H = 13*√3

Then if we steep on the 30° angle, the adjacent cathetus is x.

If we use the first relation we get:

cos(30°) = x/(13*√3)

With this, we can find the value of x.

We know that cos(30°) = (√3/√2)

Then:

(√3/√2) =  x/(13*√3)

then:

(√3/√2)*(13*√3) = x = (√3*√3)*13/√2 = 3*13/√2 = 39/√2

x = 39/√2

Now if we use the angle of 60°, the adjacent side is y.

Then:

cos(60°) = y/(13*√3)

We know that:

cos(60°) = 1/2

Then:

(1/2) = y/(13*√3)

(1/2)*(13*√3) = y

(13/2)*√3 = y

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