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 .(1 point) Responses 90.01 degrees 90.01 degrees 84.55 degrees 84.55 degrees 78.01 degrees 78.01 degrees 77.32 degrees
According to the Law of Cosines, we can use the equation:
b^2 = a^2 + c^2 - 2ac*cos(B)
Plugging in the given values,
40^2 = 9^2 + 41^2 - 2(9)(41)*cos(B)
Simplifying,
1600 = 81 + 1681 - 2(369)*cos(B)
1600 = 1762 - 738*cos(B)
-162 = -738*cos(B)
Dividing both sides by -738,
cos(B) = 162/738
cos(B) = 0.2195
To find B, we need to take the inverse cosine of 0.2195:
B = cos^(-1)(0.2195)
Using a calculator:
B = 78.01 degrees
Therefore, the value of angle B in this right triangle is 78.01 degrees.