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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Pythagorean Theorem", "Right Triangle Geometry" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem", "Right Triangle Geometry" ] } ## Identify the given side lengths Using the *Right Triangle Geometry* knowledge point $$ \begin{aligned} &\text{Vertical leg } a = 44\ &\text{Horizontal leg } b = 52\ &\text{Hypotenuse } c = ? \end{aligned} $$ ## Apply the relation to find the hypotenuse Using the *Pythagorean Theorem* knowledge point $$ \begin{aligned} &c^2 = a^2 + b^2\ &c^2 = 44^2 + 52^2\ &c^2 = 1936 + 2704\ &c^2 = 4640\ &c = \sqrt{4640} = 4\sqrt{290} \approx 68.12 \end{aligned} $$ The length of the missing side is $4\sqrt{290}$ (or approximately $68.12$). { "elements": [ { "type": "point", "params": [[0, 0]], "properties": { "name": "C", "color": "#583C87", "withLabel": false } }, { "type": "point", "params": [[0, 4.4]], "properties": { "name": "A", "color": "#583C87", "withLabel": false } }, { "type": "point", "params": [[5.2, 0]], "properties": { "name": "B", "color": "#583C87", "withLabel": false } }, { "type": "polygon", "params": [[0, 0], [5.2, 0], [0, 4.4]], "properties": { "fillColor": "rgba(140, 85, 242, 0.15)", "strokeColor": "#8C55F2", "strokeWidth": 3 } }, { "type": "text", "params": [-0.6, 2.2, "44"], "properties": { "color": "#583C87" } }, { "type": "text", "params": [2.6, -0.4, "52"], "properties": { "color": "#583C87" } }, { "type": "text", "params": [2.8, 2.4, "?"], "properties": { "color": "#F2557F" } } ] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Pythagorean Theorem" ] }

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Identify the given side lengths

Apply the relation to find the hypotenuse

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