Question

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°

Answer 1

Sides are 3 : 3√3 : 6 = 1 : √3 : 2, a 30°-60°-90° ratio. The side 6 (largest) is opposite ∠U, so ∠U = 90°. The side 3 is opposite ∠W, so ∠W = 30°, leaving ∠V = 60°.

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