calculating triangle side lengths
use the distance formula to find the lengths of the sides (\overline{ac} and \overline{ae}) that include the overlapping angle.
the length of \overline{ac} is \sqrt{2}.
the length of \overline{ae} is \sqrt{2}.

Question

calculating triangle side lengths
use the distance formula to find the lengths of the sides (\overline{ac} and \overline{ae}) that include the overlapping angle.
the length of \overline{ac} is  \sqrt{2}.
the length of \overline{ae} is  \sqrt{2}.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Distance Formula", "Coordinate Geometry" ], "new_concepts": [], "current_concepts": [ "Distance Formula", "Coordinate Geometry" ] } ## Calculate the length of AC $$ \begin{aligned} A &= (3, 1),\quad C = (5, 3) \ AC &= \sqrt{(5 - 3)^2 + (3 - 1)^2} \ AC &= \sqrt{2^2 + 2^2} = \sqrt{8} = 2\sqrt{2} \end{aligned} $$ ## Calculate the length of AE $$ \begin{aligned} A &= (3, 1),\quad E = (7, 5) \ AE &= \sqrt{(7 - 3)^2 + (5 - 1)^2} \ AE &= \sqrt{4^2 + 4^2} = \sqrt{32} = 4\sqrt{2} \end{aligned} $$ Use the distance formula to find the lengths of the sides ($\overline{AC}$ and $\overline{AE}$) that include the overlapping angle. The length of $\overline{AC}$ is 2$\sqrt{2}$. The length of $\overline{AE}$ is 4$\sqrt{2}$. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Distance Formula" ] }

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Calculate the length of AC

Calculate the length of AE

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