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