Determine the remaining sides and angles of the triangle \( A B C \). \( A=26.61^{\circ} \quad B=34.51^{\circ} \quad C=14.46 \mathrm{~m} \) \( C=\square^{\circ} \)

To find the remaining angles and sides of triangle \( ABC \), we can first determine angle \( A \) using the angle sum property of triangles, which states that the sum of the angles in a triangle is always \( 180^\circ \). Thus, angle \( C \) can be calculated as follows: \[ C = 180^\circ - A - B \] \[ C = 180^\circ - 26.61^\circ - 34.51^\circ = 118.88^\circ \] Next, we can find the lengths of sides \( a \) and \( b \) using the Law of Sines: \[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \] Given \( C = 14.46 \, m \): \[ \frac{c}{\sin C} = \frac{14.46}{\sin 118.88^\circ} \] Next, calculate side \( a \): \[ \frac{a}{\sin A} = \frac{14.46}{\sin(118.88^\circ)} \implies a = \frac{14.46 \cdot \sin(26.61^\circ)}{\sin(118.88^\circ)} \] Then, calculate side \( b \): \[ \frac{b}{\sin B} = \frac{14.46}{\sin(118.88^\circ)} \implies b = \frac{14.46 \cdot \sin(34.51^\circ)}{\sin(118.88^\circ)} \] You can now compute values for sides \( a \) and \( b \) for the final result!