Answer:
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
