Question

If cos A/a = Cos B/b = Cos C/c and if a = the area of triangle ABC, whoever solves this is a genius.

a. A = B = C
b. A ≠ B ≠ C
c. A + B + C = 180°
d. A = 90°

Answer 1

The triangle ABC is an equilateral triangle with all angles equal to 60 degrees.

Step-by-step explanation:

In this question, we are given that cos A/a = Cos B/b = Cos C/c and a = the area of triangle ABC. From these conditions, we can deduce that the triangle ABC is an equilateral triangle with all angles equal to 60 degrees (option A).

Here's how we can prove it:

1. Since cos A/a = Cos B/b = Cos C/c, the numerator and denominator for each ratio must be constant.
2. Therefore, if we consider the area of the triangle, a, we can represent it as a = k(cos A)² = k(cos B)² = k(cos C)² (where k is a constant).
3. To simplify the equation, we can substitute k for 1, giving us a = (cos A)² = (cos B)² = (cos C)².
4. Since the cosine of an angle can only be between -1 and 1, then the only possible angle that satisfies this equation is cos A = cos B = cos C = 1.
5. By using the inverse cosine function, we find that A = B = C = 60 degrees.

Therefore, the correct answer is option A: A = B = C.