Answer:
 17.2 ft
Step-by-step explanation:
The angle that the fence makes opposite the wall is ...
 180° -45° -65° = 70°
The law of cosines can be used to find the lengths of fence needed.
The fence opposite the 45° angle will have a length of ...
 short side = (10 ft)·sin(45°)/sin(70°) = 7.525 . . . feet
The fence opposite the 65° angle will have a length of ...
 long side = (10 ft)·sin(65°)/sin(70°) = 9.645 . . . feet
Then the total length of fence required is ...
 7.525 ft +9.645 ft = 17.170 ft
About 17.2 feet of chain-link fence is required to complete the enclosure.
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We have assumed there is no chain-link fence along the 10 ft wall.
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The Law of Sines tells you that for sides a, b, c and opposite angles A, B, C, you have ...
 a/sin(A) = b/sin(B) = c/sin(C)
For some given side 'a' and opposite angle A, the other two sides can be found from their opposite angles as ...
 b = sin(B)·a/sin(A)
 c = sin(C)·a/sin(A)
