Suppose that sin(t) = x/(x + 3)

Question

Use this information and a reference triangle to eliminate the trigonometric function from the following expression.
inverse tangent (x/ sqrt(6x + 9))

Answer 1

opposite leg is x
hypotenuse is x+3
so adjacent leg is √((x+3)^2 - x^2) = √(6x+9)
so tan(t) = opposite/adjacent = x/√(6x+9)

Answer 2

tan a = (x/ sqrt(6x + 9))
draw right triangle , legs x and sqrt(6x+9)
hypotenuse = sqrt (x^2 + 6 x + 9) = sqrt (x+3)^2 = x+3
then sin a = x/(x+3)