To find angle \( A \) in a right triangle using the Law of Cosines, we will substitute the values \( a = 7 \), \( b = 24 \), and \( c = 25 \) into the Law of Cosines formula:
\[ a^2 = b^2 + c^2 - 2bc \cdot \cos(A) \]
First, we need to calculate \( a^2 \), \( b^2 \), and \( c^2 \):
\[ a^2 = 7^2 = 49 \] \[ b^2 = 24^2 = 576 \] \[ c^2 = 25^2 = 625 \]
Now, substituting these values into the formula:
\[ 49 = 576 + 625 - 2 \cdot 24 \cdot 25 \cdot \cos(A) \]
Next, simplify the equation:
\[ 49 = 1201 - 1200 \cdot \cos(A) \]
Now, isolate \( \cos(A) \):
\[ 1200 \cdot \cos(A) = 1201 - 49 \] \[ 1200 \cdot \cos(A) = 1152 \] \[ \cos(A) = \frac{1152}{1200} \] \[ \cos(A) = 0.96 \]
Now, calculate angle \( A \) by taking the arccosine:
\[ A = \cos^{-1}(0.96) \]
Using a calculator:
\[ A \approx 16.3 \text{ degrees} \]
Thus, the value of angle \( A \) is approximately 16.3 degrees.
The correct response is:
16.3 degrees