14. (05.03 mc)

a 32-foot ladder is leaning against a building and forms a $29.37^\circ$ angle with the ground. how far away from the building is the base of the ladder? round your answer to the nearest hundredth. (4 points)

- 15.69 feet
- 18.01 feet
- 27.89 feet
- 36.72 feet

Question

14. (05.03 mc)

a 32-foot ladder is leaning against a building and forms a $29.37^\circ$ angle with the ground. how far away from the building is the base of the ladder? round your answer to the nearest hundredth. (4 points)

- 15.69 feet
- 18.01 feet
- 27.89 feet
- 36.72 feet

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", "Cosine Ratio" ], "new_concepts": [], "current_concepts": [ "Right Triangle Trigonometry", "Cosine Ratio" ] } ## Identify given values and target variable $$ \begin{aligned} &\text{Hypotenuse (ladder length) } c = 32\text{ feet} \ &\text{Angle with the ground } \theta = 29.37^\circ \ &\text{Adjacent side (distance from building) } x \end{aligned} $$ ## Set up the trigonometric equation $$ \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \implies \cos(29.37^\circ) = \frac{x}{32} $$ ## Solve for the unknown distance $$ \begin{aligned} &x = 32 \cdot \cos(29.37^\circ) \ &x \approx 32 \cdot 0.87148 \ &x \approx 27.887 \approx 27.89\text{ feet} \end{aligned} $$

(A) 15.69 feet

(B) 18.01 feet

(C) 27.89 feet

(D) 36.72 feet

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QUESTION IMAGE

Question

Explanation:

Identify given values and target variable

Set up the trigonometric equation

Solve for the unknown distance

Answer: