How do you find the measure of angle B in triangle ABC where the sides are given as a = 3, b = 5, and c = 7?

To find the measure of angle B in triangle ABC with sides a = 3, b = 5, and c = 7, we can use the Cosine Rule. The Cosine Rule states:

c² = a² + b² – 2ab * cos(C)

In our case, since we want to find angle B, we can rearrange the formula to solve for cos(B):

b² = a² + c² – 2ac * cos(B)

Substituting the values of sides a, b, and c:

5² = 3² + 7² – 2 * 3 * 7 * cos(B)

This simplifies to:

25 = 9 + 49 – 42 * cos(B)

Combine the numbers:

25 = 58 – 42 * cos(B)

Rearranging gives:

42 * cos(B) = 58 – 25

42 * cos(B) = 33

Now, divide both sides by 42:

cos(B) = 33 / 42

cos(B) = 0.7857 (approximately)

To find angle B, we take the inverse cosine:

B = cos^-1(0.7857)

Using a calculator, we find:

B ≈ 38.68°

Therefore, the measure of angle B in triangle ABC is approximately 38.68 degrees.