question 15 of 40

in the triangle below, what is the length of the hypotenuse?

a. 3\sqrt{2}
b. 6
c. 3\sqrt{3}
d. \sqrt{3}

Question

question 15 of 40

in the triangle below, what is the length of the hypotenuse?

a. 3\sqrt{2}
b. 6
c. 3\sqrt{3}
d. \sqrt{3}

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Trigonometric Ratios", "Sine Ratio" ], "new_concepts": [ "Special Right Triangles", "30-60-90 Triangle Theorem" ], "current_concepts": [ "Trigonometric Ratios", "Sine Ratio", "Special Right Triangles", "30-60-90 Triangle Theorem" ] } ## Identify the given values and target unknown $$ \begin{aligned} &\text{Opposite side to } 30^\circ \text{ angle } (a) = 3 \ &\text{Target unknown: Hypotenuse } (c) \end{aligned} $$ ## Apply the sine ratio $$ \begin{aligned} &\sin(30^\circ) = \frac{\text{Opposite}}{\text{Hypotenuse}} \ &\sin(30^\circ) = \frac{3}{c} \end{aligned} $$ ## Solve for the hypotenuse $$ \begin{aligned} &\frac{1}{2} = \frac{3}{c} \ &c = 6 \end{aligned} $$

A. $3\sqrt{2}$

B. 6

C. $3\sqrt{3}$

D. $\sqrt{3}$

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QUESTION IMAGE

Question

Explanation:

Identify the given values and target unknown

Apply the sine ratio

Solve for the hypotenuse

Answer: