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=18, b = 14, and c = 19. Round your answer to the nearest whole number.(1 point)
In this case, a = 18, b = 14, and c = 19.
Using the Law of Cosines variant a^2 = b^2 + c^2 - 2bc*cos(A), we can plug in the values:
18^2 = 14^2 + 19^2 - 2(14)(19)cos(A)
324 = 196 + 361 - 532cos(A)
324 = 557 - 532cos(A)
324 - 557 = - 532cos(A)
-233 = - 532cos(A)
cos(A) = -233 / -532
cos(A) = 0.437218
Then, angle A = cos^(-1)(0.437218)
Angle A ≈ 63°
Therefore, the value of angle A in the right triangle with sides a = 18, b = 14, and c = 19 is approximately 63 degrees.