a coach watches two swimmers, corey and stephen, while they practice. as corey swims directly past him, he thinks that stephen is a long way behind corey, but its hard to tell from where he is standing.

if the coach is 40 feet from corey and 50 feet from stephen, what range of distances can stephen and corey be apart?

between feet and feet.

Question

a coach watches two swimmers, corey and stephen, while they practice. as corey swims directly past him, he thinks that stephen is a long way behind corey, but its hard to tell from where he is standing.

if the coach is 40 feet from corey and 50 feet from stephen, what range of distances can stephen and corey be apart?

between   feet and   feet.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Triangle Inequality Theorem" ], "new_concepts": [], "current_concepts": [ "Triangle Inequality Theorem" ] } ## Identify the given side lengths Using the *Triangle Inequality Theorem* knowledge point $$ \begin{aligned} &a = 40 \text{ feet (distance from coach to Corey)} \ &b = 50 \text{ feet (distance from coach to Stephen)} \ &x = \text{distance between Corey and Stephen} \end{aligned} $$ ## Apply the triangle inequality bounds Using the *Triangle Inequality Theorem* knowledge point $$ \begin{aligned} &|a - b| < x < a + b \ &|40 - 50| < x < 40 + 50 \ &10 < x < 90 \end{aligned} $$ If the coach is 40 feet from Corey and 50 feet from Stephen, what range of distances can Stephen and Corey be apart? Between 10 feet and 90 feet. { "elements": [ { "type": "point", "params": [[0, 0]], "properties": { "name": "Coach", "color": "#583C87", "withLabel": true } }, { "type": "circle", "params": [[0, 0], 4.0], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 1, "dash": 2 } }, { "type": "circle", "params": [[0, 0], 5.0], "properties": { "strokeColor": "#5583F2", "strokeWidth": 1, "dash": 2 } }, { "type": "point", "params": [[4, 0]], "properties": { "name": "Corey", "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[-3, 4]], "properties": { "name": "Stephen", "color": "#5583F2", "withLabel": true } }, { "type": "segment", "params": [[0, 0], [4, 0]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "name": "40 ft", "withLabel": true } }, { "type": "segment", "params": [[0, 0], [-3, 4]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2, "name": "50 ft", "withLabel": true } }, { "type": "segment", "params": [[4, 0], [-3, 4]], "properties": { "strokeColor": "#F2557F", "strokeWidth": 2, "dash": 1, "name": "x", "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Inequality Theorem" ] }

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Question

Explanation:

Identify the given side lengths

Apply the triangle inequality bounds

Answer: