Find the acute angle $$ A $$ $$ \cos A=0.739 $$ A $$ \approx 42.3^{\circ} $$ (Round to the nearest tenth as needed.)

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To find the acute angle $$ A $$ such that $$ \cos A = 0.739 $$, follow these steps:

1. **Understand the Range:**
   - Since $$ A $$ is acute, it lies between $$ 0^\circ $$ and $$ 90^\circ $$.

2. **Use the Arccosine Function:**
   - To find $$ A $$, take the inverse cosine (arccos) of 0.739:
     $$
     A = \arccos(0.739)
     $$

3. **Calculate $$ A $$:**
   - Using a calculator, ensure it's set to degree mode.
   - Compute:
     $$
     A \approx \arccos(0.739) \approx 42.3^\circ
     $$
   
   - **Verification:**
     - **At $$ 42^\circ $$:** $$ \cos(42^\circ) \approx 0.7431 $$
     - **At $$ 43^\circ $$:** $$ \cos(43^\circ) \approx 0.7314 $$
     - Since $$ 0.739 $$ lies between $$ 0.7431 $$ and $$ 0.7314 $$, $$ A $$ is between $$ 42^\circ $$ and $$ 43^\circ $$.
     - A linear approximation gives:
       $$
       A \approx 42^\circ + \left( \frac{0.7431 - 0.739}{0.7431 - 0.7314} \right) \times 1^\circ \approx 42.3^\circ
       $$

4. **Final Answer:**
   - The acute angle $$ A $$ is approximately $$ \mathbf{42.3^\circ} $$ when rounded to the nearest tenth.
The acute angle $$ A $$ is approximately $$ 42.3^\circ $$.

Find the acute angle \( A \) \( \cos A=0.739 \) A \( \approx 42.3^{\circ} \) (Round to the nearest tenth as needed.)

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