Write the measures of its sides in ascending order in each of the following triangles:
$(1) \text{In } \Delta ABC, \angle A = 50^{\circ} \text{ and } \angle B = 60^{\circ}$
$(1) \text{In } \Delta ABC, \angle A = 50^{\circ} \text{ and } \angle B = 60^{\circ}$
(A) In $\Delta ABC$,the sum of angles is $180^{\circ}$.
Therefore,$\angle C = 180^{\circ} - (50^{\circ} + 60^{\circ}) = 180^{\circ} - 110^{\circ} = 70^{\circ}$.
We know that the side opposite to the smaller angle is smaller and the side opposite to the larger angle is larger.
The angles in ascending order are $\angle A < \angle B < \angle C$ $(50^{\circ} < 60^{\circ} < 70^{\circ})$.
Therefore,the sides in ascending order are $BC < AC < AB$.
Therefore,$\angle C = 180^{\circ} - (50^{\circ} + 60^{\circ}) = 180^{\circ} - 110^{\circ} = 70^{\circ}$.
We know that the side opposite to the smaller angle is smaller and the side opposite to the larger angle is larger.
The angles in ascending order are $\angle A < \angle B < \angle C$ $(50^{\circ} < 60^{\circ} < 70^{\circ})$.
Therefore,the sides in ascending order are $BC < AC < AB$.
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