Inverse Trigonometry Unit Test Use the stated variant of the Law of Cosines, \( a^{2}=b^{2}+c^{2}-2 b c \cdot \cos A \), to find the value of angle \( A \) in a right triangle, where \( a=8, b=15 \), and \( c=17 \). Round your answer to the nearest whole number. (1 point) \( A=\square \) degrees

To find the value of angle \( A \) in a right triangle using the Law of Cosines, we can use the formula: \[ a^{2} = b^{2} + c^{2} - 2bc \cdot \cos A \] Given: - \( a = 8 \) - \( b = 15 \) - \( c = 17 \) Substitute the given values into the formula: \[ 8^{2} = 15^{2} + 17^{2} - 2 \cdot 15 \cdot 17 \cdot \cos A \] \[ 64 = 225 + 289 - 510 \cdot \cos A \] \[ 64 = 514 - 510 \cdot \cos A \] \[ 510 \cdot \cos A = 514 - 64 \] \[ 510 \cdot \cos A = 450 \] \[ \cos A = \frac{450}{510} \] \[ \cos A = \frac{45}{51} \] Now, we can find the angle \( A \) using the inverse cosine function: \[ A = \cos^{-1}\left(\frac{45}{51}\right) \] Let's calculate the value of \( A \) in degrees. Calculate the value by following steps: - step0: Calculate: \(\arccos\left(\frac{45}{51}\right)\) - step1: Reduce the fraction: \(\arccos\left(\frac{15}{17}\right)\) The value of angle \( A \) in degrees is approximately 0.489957 radians. To convert this to degrees, we can use the conversion factor where 1 radian is approximately equal to 57.2957795 degrees. \[ A \approx 0.489957 \times 57.2957795 \] \[ A \approx 28.0 \text{ degrees} \] Therefore, the value of angle \( A \) in a right triangle is approximately 28 degrees.