Question
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
77.32 degrees
77.32 degrees
90.01 degrees
90.01 degrees
84.55 degrees
84.55 degrees
78.01 degrees
Answers
GPT 3.5
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.
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.