Question

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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

m∠V = 60°, m∠U = 90°, m∠W = 30°.

Reason: 6^2 = (3√3)^2 + 3^2 = 36, so the side 6 is the hypotenuse and ∠U = 90°. Then sin V = (opposite/hypotenuse) = (3√3)/6 = √3/2, so ∠V = 60° and ∠W = 30°.