Use the Law of Cosines, b2=a2+c2−2ac⋅cosB , to find the value of angle B in a right triangle, where a=9 , b=40 , and c=41 .
77.32 degrees
77.32 degrees
90.01 degrees
90.01 degrees
84.55 degrees
84.55 degrees
78.01 degrees
To find the value of angle B, we can use the Law of Cosines formula:
b^2 = a^2 + c^2 - 2ac * cosB
Substituting the given values:
40^2 = 9^2 + 41^2 - 2 * 9 * 41 * cosB
Simplifying:
1600 = 81 + 1681 - 738 * cosB
Combining like terms:
1600 = 1762 - 738 * cosB
Rearranging:
162 = 738 * cosB
Dividing by 738:
cosB = 162/738
Taking the inverse cosine (cos^-1) to solve for B:
B = cos^-1(162/738)
Using a calculator, we find:
B ≈ 78.01 degrees
Therefore, the answer is 78.01 degrees.