The comparison of the lengths of the sides based on the angles are given
by sine rule.
The lengths of the sides from greatest to least are;
Reasons:
The given parameters are;
∠A = 78°, ∠B = 56°, ∠C = 46°
By sine rule, we have;
[tex]\displaystyle \frac{AC}{sin(56^{\circ})} = \frac{AB}{sin(46^{\circ})} = \frac{BC}{sin(78^{\circ})}[/tex]
Given that, sin(46°) ≈ 0.719, sin(56°) ≈ 0.829, sin(78°) ≈ 0.978, we have;
sin(78°) > sin(56°) > sin(46°)
Therefore, applying equal proportions of similar ratios, we have;
BC > AC > AB
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