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
12.7 degrees
12.7 degrees
13.1 degrees
13.1 degrees
17.3 degrees
17.3 degrees
14.5 degrees
To find the value of angle A using the Law of Cosines, we can use the equation:
a^2 = b^2 + c^2 - 2bc*cos(A)
Plugging in the given values:
9^2 = 40^2 + 41^2 - 2(40)(41)*cos(A)
81 = 1600 + 1681 - 3280*cos(A)
81 = 3281 - 3280*cos(A)
3280*cos(A) = 3281 - 81
3280*cos(A) = 3200
cos(A) = 3200 / 3280
cos(A) = 0.9756
Now we need to find the inverse cosine of 0.9756 to solve for angle A. Using a calculator:
A = cos^(-1)(0.9756)
A ≈ 12.7 degrees
Therefore, the value of angle A is approximately 12.7 degrees.