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The answer to your question is 6.08 cm

Step-by-step explanation:

Start with the green triangle

             hypotenuse = 8 / cos 35

             hypotenuse = 9.77

Yellow triangle hypotenuse

              hypotenuse = (9.77 - 2.5) + 3.6

                                   = 6.2 cm

              adjacent side = 6.2 x cos 14

                                      = 6 cm

Hypotenuse of the pink triangle

              hypotenuse = (6 - 2.1) + 2.9

                                   = 3.9 + 2.9

                                   = 6.8 cm

Angle of the pink triangle

                 sin Ф = 3.8 / 6.8

                           = 0.56

                       Ф = 34°

Adjacent side of the pink triangle

            Adjacent side = 6.8 x cos 34

            Adjacent side = 5.6 cm

Adjacent side of the blue triangle

             Adjacent side = 5.6 - 3.2

                                     = 2.4 cm

Opposite side of the blue triangle

            Opposite side = 2.4 x tan 42

             Opposite side = 2.1 cm

Hypotenuse of the white triangle

             hypotenuse = 2.1 / sin 37

             hypotenuse = 3.5 cm

Hypotenuse of the yellow triangle

            hypotenuse = 4.08 + 3.5

            hypotenuse = 7.6 cm

Opposite side of the big yellow triangle

            Opposite side = 7.6 x sin 57

            Opposite side = 6.4 cm

Adjacent side of the small white triangle

           Adjacent side = 6.4 - 2.2

                                   = 4.2 cm

Hypotenuse of the small white triangle

           Hypotenuse² = 1.7² + 4.2²

           Hypotenuse² = 2.89 + 17.64

           Hypotenuse = 4.53 cm

Hypotenuse of the first pink triangle

           Hypotenuse = 4.53/ cos 20

                                 = 4.82 cm

Hypotenuse of the second pink triangle

           Hypotenuse = 4.82 + 1.5

                                 = 6.32 cm

Opposite side of the second pink triangle

          Opposite side = 6.32 x sin 74

                                   = 6.08 cm