29 in $\delta clm$ below, $m\angle c = 33^{\circ}$, $cl = 8$, and $cm = 15$.

determine and state, to the nearest tenth, the area of $\delta clm$.

Question

29 in $\delta clm$ below, $m\angle c = 33^{\circ}$, $cl = 8$, and $cm = 15$.

determine and state, to the nearest tenth, the area of $\delta clm$.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Trigonometric Area Formula" ], "current_concepts": [ "Trigonometric Area Formula", "Triangle Area" ] } ## State the given values and formula $$ \begin{aligned} &a = CL = 8\ &b = CM = 15\ &C = 33^\circ\ &\text{Area} = \frac{1}{2} a b \sin(C) \end{aligned} $$ ## Calculate the area $$ \begin{aligned} &\text{Area} = \frac{1}{2} \cdot 8 \cdot 15 \cdot \sin(33^\circ)\ &\text{Area} = 60 \cdot \sin(33^\circ)\ &\sin(33^\circ) \approx 0.544639\ &\text{Area} \approx 60 \cdot 0.544639 = 32.678 \end{aligned} $$ ## Round to the nearest tenth $$ \text{Area} \approx 32.7 $$ 32.7 { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Trigonometric Area Formula" ] }

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Question

Explanation:

State the given values and formula

Calculate the area

Round to the nearest tenth

Answer: