In a right triangle, angle c measures 40. the hypotenuse of the triangle is 10 inches long. what is the approximate length of the side adjacent to angle c

Since angle C is not 90 degrees, it's one of the acute angles
in the right triangle.

               (The side adjacent to angle C ) divided by (hypotenuse)

is the cosine of angle C .       

                    (adjacent) / (10 inches)  =  cos(40 degrees)

Multiply each side by (10 inches):

                    Adjacent side = (10 inches) x cos(40) =

                                              (10 inches)  x  0.766  = 

                                                              7.66 inches   (rounded)