Question

In triangle ABC, what is the measure of B if a = 21, b = 8, and c = 14?

Answer 1

The answer to the problem is approximately B ≈ 41.5 degrees.

Answer 2

12.97°

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Apply the Cosine Rule.

This rule states that for any triangle, where a, b, and c are the lengths of the sides, and B is the angle opposite the side of length b, the following is true:

• cos B = (a² + c² - b² ) / (2 * a * c)

Knowing that a = 21, b = 8, and c = 14, we can substitute these values into the formula.

The calculation is as follows:

• cos B = (21² + 14² - 8² ) / (2 * 21 * 14)
• cos B = 0.9744897959183674

We can use the inverse cosine to find the angle B:

• B = arccos(0.9744897959183674)
• B = 12.97°