To find the measure of angle B in triangle ABC, we can use the Law of Cosines. The Law of Cosines states that for any triangle with sides a, b, and c opposite to angles A, B, and C respectively, the following relationship holds:
c² = a² + b² – 2ab * cos(C)
We need to rearrange this formula to solving for angle B. According to the Law of Cosines, the formula for finding angle B is:
b² = a² + c² – 2ac * cos(B)
Plugging in our values, where a = 3, b = 5, and c = 7, we substitute:
5² = 3² + 7² – 2 * 3 * 7 * cos(B)
This simplifies to:
25 = 9 + 49 – 42 * cos(B)
Now simplify further:
25 = 58 – 42 * cos(B)
Next, rearranging the equation leads to:
42 * cos(B) = 58 – 25
Which simplifies to:
42 * cos(B) = 33
Dividing both sides by 42 gives:
cos(B) = 33 / 42
cos(B) = 0.7857
Finally, to find angle B, we take the arccosine of 0.7857:
B ≈ 38.68°
Therefore, the measure of angle B in triangle ABC is approximately 38.68 degrees.