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.(1 point)
Plugging in the values a=8, b=15, and c=17 into the Law of Cosines equation, we have:
8^2 = 15^2 + 17^2 - 2(15)(17)cosA
64 = 225 + 289 - 510cosA
64 = 514 - 510cosA
-450 = -510cosA
cosA = 450/510
cosA ≈ 0.8824
To find angle A, we take the inverse cosine (cos^-1) of 0.8824:
A ≈ cos^-1(0.8824)
A ≈ 28.9 degrees
Rounded to the nearest whole number, angle A ≈ 29 degrees.