To find angle \( A \) in the triangle using the Law of Cosines, we can rearrange the formula:
\[ a^2 = b^2 + c^2 - 2bc \cdot \cos A \]
Given:
- \( a = 7 \)
- \( b = 24 \)
- \( c = 25 \)
Plugging these values into the Law of Cosines, we get:
\[ 7^2 = 24^2 + 25^2 - 2 \cdot 24 \cdot 25 \cdot \cos A \]
Calculating the squares:
\[ 49 = 576 + 625 - 1200 \cdot \cos A \]
Calculating \( 24^2 + 25^2 \):
\[ 49 = 1201 - 1200 \cdot \cos A \]
Rearranging the equation to isolate \( \cos A \):
\[ 1200 \cdot \cos A = 1201 - 49 \] \[ 1200 \cdot \cos A = 1152 \] \[ \cos A = \frac{1152}{1200} \] \[ \cos A = 0.96 \]
Now, to find the angle \( A \):
\[ A = \cos^{-1}(0.96) \]
Using a calculator:
\[ A \approx 16.26 \text{ degrees} \]
Rounded to one decimal place, the angle \( A \) is approximately \( 16.3 \) degrees. Therefore, the correct response is:
16.3 degrees.