In triangle ABC, given a= 12 units, b= 22 units, c = 20 units. Determine angle B.

To find angle B in triangle ABC, we can use the Law of Cosines. The Law of Cosines states that for any triangle with sides of lengths a, b, and c, and an angle γ opposite side c, the following relationship holds:

c² = a² + b² - 2ab*cos(γ)

We can rearrange this formula to solve for cos(γ):

cos(γ) = (a² + b² - c²) / (2ab)

Substituting the given values:

cos(B) = (a² + c² - b²) / (2ac) cos(B) = (12² + 20² - 22²) / (21220) cos(B) = (144 + 400 - 484) / (480) cos(B) = 60 / 480 cos(B) = 0.125

To find the angle B, we need to find the arccosine (inverse cosine) of 0.125.

B = arccos(0.125)

Using a calculator, we find that:

B ≈ 82.82 degrees.