Use the stated variant of the Law of Cosines, b2=a2+c2−2ac⋅cosB , to find the value of side b in a right triangle, where a=3 , c=5 , and B=53.13 . Round your answer to the nearest whole number.(1 point)
Using the variant of the Law of Cosines, the formula is:
b^2 = a^2 + c^2 - 2ac*cos(B)
Given that a = 3, c = 5, and B = 53.13, we can substitute the values into the formula and solve for b:
b^2 = 3^2 + 5^2 - 2(3)(5)*cos(53.13)
b^2 = 9 + 25 - 30*cos(53.13)
b^2 = 34 - 30*cos(53.13)
Using a calculator, we can find that cos(53.13) is approximately 0.6018.
b^2 = 34 - 30*0.6018
b^2 = 34 - 18.054
b^2 ≈ 15.946
To find b, we need to find the square root of both sides:
b ≈ √15.946
b ≈ 3.993
Rounding to the nearest whole number, b is approximately 4.
Therefore, the value of side b in the right triangle is 4.