solve for c.
c = ?
pythagorean theorem: $a^2 + b^2 = c^2$
round your answer to the nearest hundredth.

Question

solve for c.
c =  ?
pythagorean theorem: $a^2 + b^2 = c^2$
round your answer to the nearest hundredth.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [], "new_concepts": [ "Pythagorean Theorem" ], "current_concepts": [ "Pythagorean Theorem", "Right Triangle Geometry" ] } ## Identify the given values and formula The given right triangle has legs of length $a = 6$ and $b = 5$, and hypotenuse $c$. The Pythagorean Theorem is: $$a^2 + b^2 = c^2$$ ## Substitute the values and solve for c $$ \begin{aligned} 6^2 + 5^2 &= c^2 \ 36 + 25 &= c^2 \ 61 &= c^2 \ c &= \sqrt{61} \end{aligned} $$ ## Calculate the decimal value and round to the nearest hundredth $$ \begin{aligned} c &\approx 7.8102 \ c &\approx 7.81 \end{aligned} $$ Solve for c. $c =$ 7.81 { "elements": [ { "type": "polygon", "params": [[0, 0], [6, 0], [6, 5]], "properties": { "fillColor": "rgba(140, 85, 242, 0.1)", "strokeColor": "#8C55F2", "strokeWidth": 2 } }, { "type": "point", "params": [[0, 0]], "properties": { "name": "", "visible": false } }, { "type": "point", "params": [[6, 0]], "properties": { "name": "", "visible": false } }, { "type": "point", "params": [[6, 5]], "properties": { "name": "", "visible": false } }, { "type": "text", "params": [3, -0.5, "6"], "properties": { "fixed": true } }, { "type": "text", "params": [6.3, 2.5, "5"], "properties": { "fixed": true } }, { "type": "text", "params": [2.7, 2.8, "c"], "properties": { "fixed": true } }, { "type": "polygon", "params": [[5.6, 0], [5.6, 0.4], [6, 0.4]], "properties": { "fillColor": "none", "strokeColor": "#8C55F2", "strokeWidth": 1 } } ] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Pythagorean Theorem" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the given values and formula

Substitute the values and solve for c

Calculate the decimal value and round to the nearest hundredth

Answer: