Use the stated variant of the Law of Cosines, a2=b2+c2−2bc⋅cosA , 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.
Using the Law of Cosines variant a² = b² + c² - 2bc cos(A), we plug in the values a = 8, b = 15, and c = 17:
8² = 15² + 17² - 2(15)(17)cos(A)
64 = 225 + 289 - 510cos(A)
64 = 514 - 510cos(A)
-450 = -510cos(A)
cos(A) = 450/510
cos(A) = 0.882352941
Taking the inverse cosine of 0.882352941, we get A = 28 degrees.
Therefore, angle A is approximately 28 degrees.