the figure below shows a triangular piece of cloth:
what is the length of the portion bc of the cloth?

- $8 \cos 35^\circ$
- $\frac{\sin 35^\circ}{8}$
- $\frac{\cos 35^\circ}{8}$
- $8 \sin 35^\circ$

Question

the figure below shows a triangular piece of cloth:
what is the length of the portion bc of the cloth?

- $8 \cos 35^\circ$
- $\frac{\sin 35^\circ}{8}$
- $\frac{\cos 35^\circ}{8}$
- $8 \sin 35^\circ$

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": [ "Right Triangle Trigonometry", "Sine Ratio" ], "current_concepts": [ "Right Triangle Trigonometry", "Sine Ratio" ] } ## Identify the given values and the target side $$ \begin{aligned} &\text{Triangle } ABC \text{ is a right triangle with } \angle B = 90^\circ\ &\text{Hypotenuse } AC = 8\text{ in.}\ &\text{Angle } A = 35^\circ\ &\text{Opposite side to } \angle A = BC \end{aligned} $$ ## Apply the trigonometric ratio for sine $$ \begin{aligned} &\sin(A) = \frac{\text{Opposite}}{\text{Hypotenuse}}\ &\sin(35^\circ) = \frac{BC}{8} \end{aligned} $$ ## Solve for the length of BC $$ BC = 8 \sin 35^\circ $$

(A) $8 \cos 35^\circ$

(B) $\frac{\sin 35^\circ}{8}$

(C) $\frac{\cos 35^\circ}{8}$

(D) $8 \sin 35^\circ$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Right Triangle Trigonometry" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given values and the target side

Apply the trigonometric ratio for sine

Solve for the length of BC

Answer: