$\delta abc$ has the following angle measurements:

$\angle a = 45^{\circ}$
$\angle b = 60^{\circ}$
$\angle c = 75^{\circ}$

which of the following is the smallest side of this triangle?

* $\overline{ac}$
* $\overline{ab}$
* $\overline{ba}$
* $\overline{bc}$

Question

$\delta abc$ has the following angle measurements:

$\angle a = 45^{\circ}$
$\angle b = 60^{\circ}$
$\angle c = 75^{\circ}$

which of the following is the smallest side of this triangle?

* $\overline{ac}$
* $\overline{ab}$
* $\overline{ba}$
* $\overline{bc}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Angle-Side Relationship" ], "current_concepts": [ "Angle-Side Relationship" ] } ## Identify the given angle measurements $$ \begin{aligned} \angle A &= 45^\circ \ \angle B &= 60^\circ \ \angle C &= 75^\circ \end{aligned} $$ ## Compare the angle sizes to find the smallest angle $$ 45^\circ < 60^\circ < 75^\circ \implies \angle A < \angle B < \angle C $$ The smallest angle is $\angle A$. ## Determine the side opposite to the smallest angle In $\triangle ABC$, the side opposite to $\angle A$ is $\overline{BC}$. By the angle-side relationship in a triangle, the shortest side is opposite the smallest angle. Therefore, the smallest side is $\overline{BC}$.

(A) $\overline{AC}$

(B) $\overline{AB}$

(C) $\overline{BA}$

(D) $\overline{BC}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Angle-Side Relationship" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given angle measurements

Compare the angle sizes to find the smallest angle

Determine the side opposite to the smallest angle

Answer: