Question

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

Answer 1

2 sqrt(3) = n

k = 4 sqrt(3)

Explanation:

We know that cos 30 = adjacent/ hypotenuse

cos 30 = 6 /k

Multiply each side by k

k cos 30 = 6k * k

k cos 30 = 6

Divide each side by cos 30

k cos 30/ cos 30 = 6/ cos 30

k = 6 / cos 30

k = 6/ (sqrt(3)/2)

k =12 / sqrt(3)

We cannot leave the sqrt in the denominator

k = 12 / sqrt(3) * sqrt(3)/sqrt(3)

k = 12 sqrt(3)/3

k = 4 sqrt(3)

We know tan 30 = opposite/adjacent

tan 30 = n/6

Multiply each side by 6

6 tan 30 = n

6 * (sqrt(3)/3) = n

6/3 * sqrt(3) = n

2 sqrt(3) = n