what is the length of the unknown leg in the right triangle?

* (3\text{ ft})
* (\sqrt{57}\text{ ft})
* (\sqrt{65}\text{ ft})
* (9\text{ ft})

Question

what is the length of the unknown leg in the right triangle?

* (3\text{ ft})
* (\sqrt{57}\text{ ft})
* (\sqrt{65}\text{ ft})
* (9\text{ ft})

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Pythagorean Theorem" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem" ] } ## Apply the Pythagorean theorem $$ a^2 + b^2 = c^2 $$ ## Substitute the given values $$ \begin{aligned} a^2 + 8^2 &= (\sqrt{73})^2 \ a^2 + 64 &= 73 \end{aligned} $$ ## Solve for the unknown leg length $$ \begin{aligned} a^2 &= 73 - 64 \ a^2 &= 9 \ a &= 3\text{ ft} \end{aligned} $$

(A) 3 ft

(B) $\sqrt{57}$ ft

(C) $\sqrt{65}$ ft

(D) 9 ft

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QUESTION IMAGE

Question

Explanation:

Apply the Pythagorean theorem

Substitute the given values

Solve for the unknown leg length

Answer: