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

$\sqrt{22}\text{ mi}$
$\sqrt{32}\text{ mi}$
$\sqrt{104}\text{ mi}$
$\sqrt{194}\text{ mi}$

Question

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

$\sqrt{22}\text{ mi}$
$\sqrt{32}\text{ mi}$
$\sqrt{104}\text{ mi}$
$\sqrt{194}\text{ mi}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Pythagorean Theorem" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem", "Radical Equations" ] } ## Set up the Pythagorean equation $$ a^2 + 9^2 = (\sqrt{113})^2 $$ ## Solve for the unknown leg $$ \begin{aligned} a^2 + 81 &= 113 \ a^2 &= 113 - 81 \ a^2 &= 32 \ a &= \sqrt{32} \end{aligned} $$

(A) $\sqrt{22}\text{ mi}$

(B) $\sqrt{32}\text{ mi}$

(C) $\sqrt{104}\text{ mi}$

(D) $\sqrt{194}\text{ mi}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Pythagorean Theorem" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set up the Pythagorean equation

Solve for the unknown leg

Answer: