Kim is building a triangular dog pen. She will use an existing 10 m wall as one side. She will then build a fence going out at a 45° angle on one side of the wall and a 65° angle on the other side. How much chain-link fence is needed to complete the fence?
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  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.

_____

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)

answer: the correct answer is -32

step-by-step explanation: