Question

In \( \triangle ABC \), if \( \frac{\cos A}{a} = \frac{\cos B}{b} = \frac{\cos C}{c} \) with usual notations, then the triangle is:

• A. an isosceles triangle
• B. an equilateral triangle
• C. a right-angled scalene triangle
• D. a scalene triangle

Hint:

When the ratios of the cosines of angles to the lengths of the opposite sides are equal, it indicates an equilateral triangle.

Answer 1

The Correct Option is B

Step 1: Analyze the given condition.
We are given that: \[ \frac{\cos A}{a} = \frac{\cos B}{b} = \frac{\cos C}{c} \] This implies a symmetry in the triangle. In any triangle, this condition can only hold if the angles are all equal and the sides are proportional. Step 2: Conclusion.
Since the angles are equal, the triangle is an equilateral triangle. Thus, the correct answer is \( \boxed{\text{an equilateral triangle}} \).