find $a$.

\a^2 + \text{___}^2 = \text{___}^2\
\a^2 + \text{___} = \text{___}\
\a^2 = \text{___}\
\a = \sqrt{\text{___}} = \text{___}\

Question

find $a$.

\a^2 + \text{___}^2 = \text{___}^2\
\a^2 + \text{___} = \text{___}\
\a^2 = \text{___}\
\a = \sqrt{\text{___}} = \text{___}\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Pythagorean Theorem" ], "new_concepts": [ "Simplifying Radicals" ], "current_concepts": [ "Pythagorean Theorem", "Simplifying Radicals" ] } ## Apply the Pythagorean theorem $$ \begin{aligned} a^2 + 8^2 &= (\sqrt{80})^2 \ a^2 + 64 &= 80 \end{aligned} $$ ## Solve for a $$ \begin{aligned} a^2 &= 80 - 64 \ a^2 &= 16 \ a &= 4 \end{aligned} $$ Find $a$. $$a^2 + 8^2 = (\sqrt{80})^2$$ $$a^2 + 64 = 80$$ $$a^2 = 16$$ $a =$ 4 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Pythagorean Theorem" ] }

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Explanation:

Apply the Pythagorean theorem

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