the lengths of the legs of a right triangle are given. find the hypotenuse.

(a = 8), (b = 15)

the length of the hypotenuse, (c), is

Question

the lengths of the legs of a right triangle are given. find the hypotenuse.

(a = 8), (b = 15)

the length of the hypotenuse, (c), is

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Pythagorean Theorem", "Right Triangle Geometry" ], "current_concepts": [ "Pythagorean Theorem", "Right Triangle Geometry" ] } ## State the Pythagorean theorem formula $$ a^2 + b^2 = c^2 $$ ## Substitute the given leg lengths $$ \begin{aligned} a &= 8 \ b &= 15 \ 8^2 + 15^2 &= c^2 \end{aligned} $$ ## Solve for the hypotenuse $$ \begin{aligned} 64 + 225 &= c^2 \ 289 &= c^2 \ c &= \sqrt{289} \ c &= 17 \end{aligned} $$ The length of the hypotenuse, c, is 17. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Pythagorean Theorem" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

State the Pythagorean theorem formula

Substitute the given leg lengths

Solve for the hypotenuse

Answer: