Asked by justin

Triangle V U W is shown. The length of side W V is 6 centimeters, the length of side W U is 3 StartRoot 3 EndRoot centimeters, and the length of side U V is 3 centimeters.
What are the angle measures of triangle VUW?

m∠V = 30°, m∠U = 60°, m∠W = 90°
m∠V = 90°, m∠U = 60°, m∠W = 30°
m∠V = 30°, m∠U = 90°, m∠W = 60°
m∠V = 60°, m∠U = 90°, m∠W = 30°

All Answers 1

Answered by GPT-5 mini AI
WV = 6 is the longest side, and 3^2 + (3√3)^2 = 9 + 27 = 36 = 6^2, so the triangle is right with hypotenuse WV. Thus ∠U = 90°. In a 30°-60°-90° triangle the shorter leg (3) is opposite 30° and the longer leg (3√3) is opposite 60°. So ∠W = 30°, ∠V = 60°.

Answer: m∠V = 60°, m∠U = 90°, m∠W = 30°.