\( \left. \begin{array} { l } { a = C = 21 cm , a = 14 cm , A = 60 ^ { \circ } } \\ { b = A = 40 ^ { \circ } , C = 78 , c = 14 cm } \\ { c = A = 29 ^ { \circ } , b = 4 cm , c = 3 cm } \\ { d = a = 21 cm , b = 16,6 cm , c = 10,3 cm } \end{array} \right. \)

It seems like you have provided a list of triangles with their respective sides and angles. Let's analyze each triangle based on the information given. 1. **Triangle 1:** - \( a = 21 \, \text{cm} \) - \( C = 21 \, \text{cm} \) - \( A = 60^\circ \) To find the remaining angle \( B \) and side \( b \), we can use the Law of Sines: \[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \] Since \( C = 21 \, \text{cm} \) is given, we need to find \( b \) and \( B \). 2. **Triangle 2:** - \( b = 40^\circ \) - \( C = 78^\circ \) - \( c = 14 \, \text{cm} \) First, we can find angle \( A \): \[ A = 180^\circ - B - C = 180^\circ - 40^\circ - 78^\circ = 62^\circ \] Now we can use the Law of Sines to find side \( a \): \[ \frac{a}{\sin A} = \frac{c}{\sin C} \] \[ a = \frac{c \cdot \sin A}{\sin C} = \frac{14 \cdot \sin(62^\circ)}{\sin(78^\circ)} \] 3. **Triangle 3:** - \( A = 29^\circ \) - \( b = 4 \, \text{cm} \) - \( c = 3 \, \text{cm} \) We can find angle \( C \) using the Law of Sines: \[ \frac{b}{\sin B} = \frac{c}{\sin C} \] We can also find angle \( B \) using: \[ B = 180^\circ - A - C \] 4. **Triangle 4:** - \( a = 21 \, \text{cm} \) - \( b = 16.6 \, \text{cm} \) - \( c = 10.3 \, \text{cm} \) We can use the Law of Cosines to find angles \( A \), \( B \), and \( C \): \[ c^2 = a^2 + b^2 - 2ab \cos C \] Rearranging gives: \[ \cos C = \frac{a^2 + b^2 - c^2}{2ab} \] If you need specific calculations or further analysis on any of these triangles, please let me know!