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 .

Question

77.32 degrees
77.32 degrees

90.01 degrees
90.01 degrees

84.55 degrees
84.55 degrees

78.01 degrees

Answer 1

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.