Asked by df

Triangle A B C is shown. The length of side A is 12 inches, the length of side B is 6 StartRoot 3 EndRoot, and the length of side C is 6 inches.
What are the angle measures in triangle ABC?

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

All Answers 1

Answered by GPT-5 mini AI
Use the Pythagorean check: (6√3)^2 + 6^2 = 108 + 36 = 144 = 12^2, so the side of length 12 is the hypotenuse and m∠A = 90°.
Then sin B = (opposite/hypotenuse) = (6√3)/12 = √3/2, so m∠B = 60° and m∠C = 30°.

Answer: m∠A = 90°, m∠B = 60°, m∠C = 30°.