a = 9, b = 3, and c = 11. Use the law of Cosines to solve B.
My ans: 12.90 degs?
Approximately correct answer.
cos B = ( a ^ 2 + c ^ 2 - b ^ 2 ) / ( 2 a c ) =
( 9 ^ 2 + 11 ^ 2 - 3 ^ 2 ) / ( 2 * 9 * 11 ) =
( 81 + 121 - 9 ) / 198 =
193 / 198 = 0.97474747
B = cos ^ - 1 ( 0.97474747 )
B = 12,90352 °
B = 12 ° 54 ' 12.672 "
B = 12 ° 54 ' 13 " rouneded at seconds
To solve for angle B using the law of cosines, we need to have the lengths of all three sides of the triangle. In this case, if we have side lengths a = 9, b = 3, and c = 11, we can use the formula for the law of cosines:
c^2 = a^2 + b^2 - 2ab * cos(B)
To solve for angle B, we rearrange the formula and isolate cos(B):
cos(B) = (a^2 + b^2 - c^2) / (2ab)
Substituting the given values:
cos(B) = (9^2 + 3^2 - 11^2) / (2*9*3)
cos(B) = (81 + 9 - 121) / 54
cos(B) = -31 / 54
Next, we need to find the inverse cosine (cos^-1) of -31/54 to find angle B:
B = cos^-1(-31/54)
B ≈ 112.11 degrees
So, the correct answer is approximately 112.11 degrees, not 12.90 degrees.