Applying the trigonometry ratios, the missing lengths for right triangle ABC are: 12 and 8√3.
<h3>What is Trigonometry Ratios?</h3>
Trigonometric ratios are defined as the values of all trigonometric functions based on the right-angled triangle's side ratio. The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.
<h3>According to the given information:</h3>
Reference angle (∅) = 60
Adjacent = 4√3
Opposite = ?
<h3>Apply TOA:</h3>
tan 60 = opp/adj
tan 60 = Opp/4√3
√3 = opp/4√3
Opposite = √3 × 4√3
Opposite = 12
<h3>Find the other missing side:</h3>
Reference angle (∅) = 60
Adjacent = 4√3
Hypotenuse = ?
<h3>Apply CAH:</h3>
cos 60 = adj/hyp
cos 60 = 4√3/hyp
hyp = 4√3/cos 60
hyp = 4√3/1/2
hyp = 4√3 × 2
hyp = 8√3
Therefore, applying the trigonometry ratios, the missing lengths for right triangle ABC are: 12 and 8√3.
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