To find the angle \( A \) in the triangle using the Law of Cosines, we can rearrange the Law of Cosines formula:
\[ a^2 = b^2 + c^2 - 2bc \cdot \cos A \]
From rearranging this formula, we can solve for \( \cos A \):
\[ \cos A = \frac{b^2 + c^2 - a^2}{2bc} \]
Given:
- \( a = 7 \)
- \( b = 24 \)
- \( c = 25 \)
Now we can calculate:
- Calculate \( b^2 \) and \( c^2 \):
\[ b^2 = 24^2 = 576 \] \[ c^2 = 25^2 = 625 \]
- Calculate \( a^2 \):
\[ a^2 = 7^2 = 49 \]
- Substitute these values into the formula for \( \cos A \):
\[ \cos A = \frac{576 + 625 - 49}{2 \cdot 24 \cdot 25} \] \[ \cos A = \frac{1152}{1200} \] \[ \cos A = 0.96 \]
- Now calculate \( A \) by taking the arccosine:
\[ A = \cos^{-1}(0.96) \]
Using a calculator:
\[ A \approx 15.9 \text{ degrees} \]
This is close to the option of \( 16.3 \) degrees. Thus, the angle \( A \) is approximately \( 16.3 \) degrees.
The correct response is:
16.3 degrees