Idon't understand how sine, cosine, and tangent have anything to do with solving these? ?

Sin of an angle=opposite side/hypotenuese
cos of an angle=adjacent side/ hypotenuese
tan of an angle=opposite side / adjacent side
11. sine M=7/25            12. do the same but using the number of this triangle
      cos  M=24/25
      tan  M=7/24

14. They give you the angle 35 degrees. So that will be what you start with. Look at the lengths of the sides given. Where are they located in respect to the angle 35.  20 is the hypoteneuse, and x is opposite of 35. So the equation that uses hypoteneuse and opposite is sin. 
 sin 35=35/x, punch in sin 35 into the calculator. then you would get .57=35/x. The cross multiply .57x=35=61.40.

Now you can repeat for the rest of the problems. I hope this is helpful.

Top right since it passes vertical line test