laura is visiting new york city and decides to go up the empire state building to get a good view of the city, including views of the statue of liberty and the world trade center. she overhears a tour guide saying that the empire state building is around 4 miles from the world trade center. her brochure map states that the world trade center is 2 miles from the statue of liberty. if the three landmarks create a triangle, between what two distances is she currently from the statue of liberty?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Triangle Inequality Theorem" ], "new_concepts": [], "current_concepts": [ "Triangle Inequality Theorem" ] } ## Identify the given side lengths Using the *Triangle Inequality Theorem* knowledge point $$ \begin{aligned} &a = 4 \text{ miles (Empire State Building to World Trade Center)} \ &b = 2 \text{ miles (World Trade Center to Statue of Liberty)} \ &x = \text{distance from Empire State Building to Statue of Liberty} \end{aligned} $$ ## Apply the triangle inequality bounds Using the *Triangle Inequality Theorem* knowledge point $$ \begin{aligned} &|a - b| < x < a + b \ &|4 - 2| < x < 4 + 2 \ &2 < x < 6 \end{aligned} $$ Between 2 miles and 6 miles { "subject": "Mathematics", "question_type": "Word Problem", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Inequality Theorem" ] }

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Explanation:

Identify the given side lengths

Apply the triangle inequality bounds

Answer: