Which equations could be used to solve for the unknown lengths of △ABC? Check all that apply.
sin(45°) = BC/9
sin(45°) = 9/BC
9 tan(45°) = AC 
(AC)sin(45°) = BC
cos(45°) = BC/9

Solution:

The only equation that can be used to find the unknown lengths of △ABC is the following:

sin(45°) = BC/9

From the above figure

Using trignometric ratios,

sin45° = Perpendicular/Hypotenuse

= BC/9

Here if we consider θ as 45°, then perpendicular will be side opposite to the angle which is BC and hypotenuse is 9.

That is why the correct equation is sin (45°) = BC/9.

The rest of the equations are not compatible with the diagram.

Which equations could be used to solve for the unknown lengths of △ABC? Check all that apply.

Summary:

The equation which could be used to solve the unknown lengths of the right angled triangle △ABC is sin(45°) = BC/9.