The length of the hypotenuse line segment AC in right triangle ABC is 25 cm. The length of line segment BC is 15 centimeters. What is the approximate measure of angle ACB?

From my understanding you ahould use the trig function cos to solve this.
cos(c) = 15/25 or 0.6
if you have this following function on your calculator I suggest using it:

cos ^{ - 1}

by using the function like so:

cos^{ - 1} (0.6

you should get about 53.13° (rounding to the nearest hundredth)
Hope this helped.