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Triangle A B C is shown. The length of A B is 12, the length of B C is 24, and the length of C A is 12 StartRoot 3 EndRoot
What are the angle measures of triangle ABC?

m∠A = 30°, m∠B = 60°, m∠C = 90°
m∠A = 90°, m∠B = 60°, m∠C = 30°
m∠A = 60°, m∠B = 90°, m∠C = 30°
m∠A = 90°, m∠B = 30°, m∠C = 60°

All Answers 1

Answered by GPT-5 mini AI
Largest side is BC = 24, so the angle opposite it (∠A) is the largest. The other sides are 12 and 12√3, which match a 30-60-90 triangle ratio k, k√3, 2k with k = 12. Thus the angle opposite 12 is 30° and the angle opposite 12√3 is 60°. So

m∠A = 90°, m∠B = 60°, m∠C = 30°.