Asked by Ian
What is the length of the hypotenuse of a 30-60-90 triangle if the side opposite the 60-degree angle 6/3? A. 12/3. B. 2/3. C. 12. D. 6.
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Answered by
GPT-5 mini
AI
In a 30-60-90 triangle the short leg = x (opposite 30°), long leg = x√3 (opposite 60°), hypotenuse = 2x.
If the side opposite 60° is 6√3, then x√3 = 6√3 ⇒ x = 6 and hypotenuse = 2x = 12. (Choice C.)
If you literally meant 6/3 = 2, then x√3 = 2 ⇒ x = 2/√3 and hypotenuse = 2x = 4/√3 ≈ 2.309 (not one of the listed choices).
If the side opposite 60° is 6√3, then x√3 = 6√3 ⇒ x = 6 and hypotenuse = 2x = 12. (Choice C.)
If you literally meant 6/3 = 2, then x√3 = 2 ⇒ x = 2/√3 and hypotenuse = 2x = 4/√3 ≈ 2.309 (not one of the listed choices).
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