Question

A new landowner has a triangular piece of flat land she wishes to fence. Starting at the first corner, she measures the first side to be 5.7 m long and is directed 0.8 radians north of east. From the second corner, the second side is 8 m long and is directed 0.6 radians west of north. What is the length of the third side of the fence?

Answer 1

A = 5.7 ( cos 0.8 i +sin 0.8 j) =3.97 i + 4.09 j

B = 8 ( - sin 0.6 i + cos 0.6 j) = - 4.517 i + 6.6 j

in order to find third side, let have the total displacement of the triangle finally must be 0

A + B + C = 0

C = (4.517 - 3.97) i + ( - 6.6 - 4.09) j

C = 0.547 i - 10.69 j

magnitude of side

C = 10.7 m

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