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
First, substitute the given values into the formula:
8^2 = 15^2 + 17^2 - 2(15)(17)cosA
64 = 225 + 289 - 510cosA
64 = 514 - 510cosA
-450 = -510cosA
cosA = -450/-510
cosA = 15/17
Now, use the inverse cosine function to find angle A:
A = cos^(-1)(15/17)
A ≈ 29 degrees
Therefore, angle A ≈ 29 degrees.