Tangent Divergence?

📌 CONCEPT: The tangent of an angle in a right-angled triangle is greater than the angle itself when the angle is less than 45 degrees.

📐 RULE / FORMULA: In a right-angled triangle, tan(angle) > angle when 0° < angle < 45°.

💡 WORKED EXAMPLE: Consider a right-angled triangle ABC with ∠A = 30°. We have tan(30°) = √3 and 30° < 45°. Therefore, the tangent of ∠A is greater than the angle itself.

⚠️ COMMON MISTAKE: Students often mistakenly assume that the tangent of an angle is greater than the angle itself for all angles less than 90°, but this is not true. The tangent of an angle is greater than the angle itself only when the angle is less than 45°.