7. (05.02 mc)

find the measure of angle y. round your answer to the nearest hundredth. (please type the numerical answer only) (4 points)

Question

7. (05.02 mc)

find the measure of angle y. round your answer to the nearest hundredth. (please type the numerical answer only) (4 points)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Right Triangle Trigonometry", "Sine Ratio", "Inverse Trigonometric Functions" ], "new_concepts": [], "current_concepts": [ "Right Triangle Trigonometry", "Sine Ratio", "Inverse Trigonometric Functions" ] } ## Identify the given values Using the *Right Triangle Trigonometry* knowledge point $$ \begin{aligned} &\text{Opposite side } (opp) = 4\ &\text{Hypotenuse } (hyp) = 20\ &\text{Target angle} = y^\circ \end{aligned} $$ ## Apply the sine ratio Using the *Sine Ratio* knowledge point $$ \sin(y^\circ) = \frac{opp}{hyp} = \frac{4}{20} = 0.2 $$ ## Solve for the angle Using the *Inverse Trigonometric Functions* knowledge point $$ \begin{aligned} &y = \arcsin(0.2) \approx 11.536959^\circ\ &y \approx 11.54 \end{aligned} $$ Find the measure of angle y. Round your answer to the nearest hundredth. (please type the numerical answer only) 11.54 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Right Triangle Trigonometry" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given values

Apply the sine ratio

Solve for the angle

Answer: