What is \angle B equal to?
Consider the following for the three (03) items that follow : The sides of a triangle ABC are AB=3\text{ cm}, BC=5\text{ cm} and CA=7\text{ cm}.
- A. 60°
- B. 105°
- C. 120° ✓
- D. 150°
Correct Answer: C. 120°
Explanation
Let side lengths be a=5, b=7, c=3. Using the Cosine Rule for the angle opposite to the longest side: \cos B = \frac{a^2+c^2-b^2}{2ac} = \frac{5^2+3^2-7^2}{2(5)(3)} = \frac{25+9-49}{30} = -\frac{1}{2}. Therefore, \angle B = 120^{\circ}.