How do I simplify using trig identities

Suppose y varies directly with x. write a direct variation equation that relates x and y. then find the value of y when x=12 y=7 when x=3

Two years ago a man was six times as old as his daughter. in 18 years he will be twice as old as his daughter. determine their present ages.

Prove the converse of the pythagorean theorem using similar triangles. the converse of the pythagorean theorem states that when the sum of the squares of the lengths of the legs of the triangle equals the squares length of the hypotenuse, the triangle is a right triangle. be sure to create and name the appropriate geometric figures.