the length of the shadow of a building is 100 meters, as shown below:

what is the height of the building? (1 point)

44 m
71 m
100 m
255 m

Question

the length of the shadow of a building is 100 meters, as shown below:

what is the height of the building? (1 point)

44 m
71 m
100 m
255 m

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Right Triangle Trigonometry", "Tangent Ratio" ], "new_concepts": [], "current_concepts": [ "Right Triangle Trigonometry", "Tangent Ratio" ] } ## Identify given values and target $$ \begin{aligned} &\text{Angle of elevation } (\angle C) = 45^\circ\ &\text{Adjacent side (Shadow } BC) = 100\text{ m}\ &\text{Opposite side (Building height } AB) = h \end{aligned} $$ ## Set up trigonometric equation $$ \begin{aligned} &\tan(45^\circ) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{h}{100} \end{aligned} $$ ## Solve for building height $$ \begin{aligned} &1 = \frac{h}{100}\ &h = 100\text{ m} \end{aligned} $$

44 m

71 m

100 m

255 m

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

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QUESTION IMAGE

Question

Explanation:

Identify given values and target

Set up trigonometric equation

Solve for building height

Answer: