10. (05.03 mc)

jim is designing a seesaw for a childrens park. the seesaw should make an angle of $30^\circ$ with the ground, and the maximum height to which it should rise is 2 meters, as shown below:

what is the maximum length of the seesaw? (4 points)

3 meters
3.5 meters
4 meters
4.5 meters

Question

10. (05.03 mc)

jim is designing a seesaw for a childrens park. the seesaw should make an angle of $30^\circ$ with the ground, and the maximum height to which it should rise is 2 meters, as shown below:

what is the maximum length of the seesaw? (4 points)

3 meters
3.5 meters
4 meters
4.5 meters

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Right Triangle Trigonometry", "Sine Ratio" ], "new_concepts": [], "current_concepts": [ "Right Triangle Trigonometry", "Sine Ratio" ] } ## Identify the given values and target unknown $$ \begin{aligned} &\theta = 30^\circ\ &\text{Opposite side } (h) = 2\text{ meters}\ &\text{Hypotenuse } (L) = \text{maximum length of the seesaw} \end{aligned} $$ ## Set up the trigonometric ratio $$ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} \implies \sin(30^\circ) = \frac{2}{L} $$ ## Solve for the length of the seesaw $$ \begin{aligned} &\sin(30^\circ) = 0.5\ &0.5 = \frac{2}{L}\ &L = \frac{2}{0.5} = 4\text{ meters} \end{aligned} $$

3 meters

3.5 meter

4 meters

4.5 meters

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QUESTION IMAGE

Question

Explanation:

Identify the given values and target unknown

Set up the trigonometric ratio

Solve for the length of the seesaw

Answer: