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

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.