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\\).

Explanation:

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<reasoning>

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

\[
\text{Area} \approx 32.7
\]
</reasoning>

<answer>
32.7
</answer>

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Answer:

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</pre_analysis>

<reasoning>

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

\[
\text{Area} \approx 32.7
\]
</reasoning>

<answer>
32.7
</answer>

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