an aerial camera is suspended from a blimp and positioned at d. the camera needs to cover 125 meters of ground distance and will be flown at an altitude of 75 meters. if the camera attachment to the blimp is 20 meters in length, how low should the camera hang from the blimp, from g to d?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "AA Similarity Postulate", "Triangle Similarity Statements", "Vertical Angles Theorem" ], "new_concepts": [ "Similar Triangles Applications" ], "current_concepts": [ "AA Similarity Postulate", "Triangle Similarity Statements", "Vertical Angles Theorem", "Similar Triangles Applications" ] } ## Identify the geometric relationships Using the **Vertical Angles Theorem** and **AA Similarity Postulate** knowledge points $$ \begin{aligned} &\angle FDE \cong \angle ADC \quad \text{(Vertical Angles)}\ &FE \parallel AC \implies \angle DFE \cong \angle DCA \quad \text{(Alternate Interior Angles)}\ &\triangle FDE \sim \triangle CDA \quad \text{(AA Similarity)} \end{aligned} $$ ## Set up the similarity ratio Using the **Triangle Similarity Statements** knowledge point $$ \begin{aligned} &\frac{GD}{DB} = \frac{FE}{AC}\ &\frac{GD}{75} = \frac{20}{125} \end{aligned} $$ ## Solve for the unknown height GD $$ \begin{aligned} &GD = 75 \cdot \frac{20}{125}\ &GD = 75 \cdot 0.16\ &GD = 12\text{ m} \end{aligned} $$ $12\text{ meters}$ { "subject": "Mathematics", "question_type": "Word Problem", "knowledge_point": [ "Mathematics", "Geometry", "Similar Triangles Applications" ] }

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Question

Explanation:

Identify the geometric relationships

Set up the similarity ratio

Solve for the unknown height GD

Answer: