In a triangle ABC if BC =1 and AC = 2. Then the maximum possible value of angle A is-
Question
In a triangle ABC if BC =1 and AC = 2. Then the maximum possible value of angle A is-
Solution
The maximum possible value of angle A in triangle ABC can be found using the law of cosines. The law of cosines states that c² = a² + b² - 2abcosC, where a, b, and c are the sides of the triangle and C is the angle opposite side c.
In this case, we have BC = 1, AC = 2, and we're looking for the maximum possible value of angle A. We can rearrange the law of cosines to solve for cosC:
cosC = (a² + b² - c²) / 2ab
Substituting the given values, we get:
cosA = (1² + 2² - 1²) / 212 = 2 / 4 = 0.5
Therefore, the maximum possible value of angle A is cos⁻¹(0.5) = 60 degrees.
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