Use the Law of Cosines, a2=b2+c2−2bc⋅cosA , to find the value of angle A in a right triangle, where a=9 , b=40 , and c=41 .(1 point) Responses 12.7 degrees 12.7 degrees 14.5 degrees 14.5 degrees 13.1 degrees 13.1 degrees 17.3 degrees
To find the value of angle A, we can use the Law of Cosines formula:
a^2 = b^2 + c^2 - 2bc*cosA
Substituting the given values:
9^2 = 40^2 + 41^2 - 2(40)(41)*cosA
81 = 1600 + 1681 - 3280*cosA
81 = 3281 - 3280*cosA
3280*cosA = 3281 - 81
3280*cosA = 3200
cosA = 3200 / 3280
cosA ≈ 0.9756
To find angle A, we can take the inverse cosine (arccos) of 0.9756:
A ≈ arccos(0.9756)
A ≈ 12.7 degrees
Thus, the value of angle A in the right triangle is approximately 12.7 degrees.