Question

HELP!!!! Order the lengths of the sides of ABC from greatest to least

Answer 1

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;

• BC > AC > AB

Reasons:

The given parameters are;

∠A = 78°, ∠B = 56°, ∠C = 46°

By sine rule, we have;

$\displaystyle \frac{AC}{sin(56^{\circ})} = \frac{AB}{sin(46^{\circ})} = \frac{BC}{sin(78^{\circ})}$

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

Learn more about sine rule here:

brainly.com/question/7591047