Question

Which trigonometric ratios are correct for triangle ABC? Check all that apply.

-sin(C) =
-cos(B) =
-tan(C) =
-sin(B) =
-tan(B) =

Answer 1

Assuming the - are bullet points and not negative signs:
sin = opposite/hypotenuse
cos = adjacent / hypotenuse
tan = opposite / adjacent.
Also remember the special properties of the 30 - 60 - 90 triangle.
This tells us that side AB = 9√3

Combining this info:
sin (C) = 9√3 ÷ 18 = √3 ÷ 2
cos(B) = 9 √3 ÷ 18 = √3 ÷ 2
tan(C) = 9 √3 ÷ 9 = √3
sin(B) = 9 ÷ 18 = 1/2
tan(B) = 9 ÷ 9√3 = 1 / √3 = √(3) ÷ 3