The tangent of 60 degrees (tan 60°) is equal to the square root of 3, or approximately 1.732. Here are a few ways to understand and derive this value:
1. Using a 30-60-90 Triangle:
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A 30-60-90 triangle is a special right triangle where the angles are 30°, 60°, and 90°. The sides are in the ratio 1 : √3 : 2, where:
- The side opposite the 30° angle is 1.
- The side opposite the 60° angle is √3.
- The hypotenuse (opposite the 90° angle) is 2.
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Recall that the tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. Therefore:
tan 60° = (Opposite Side) / (Adjacent Side) = √3 / 1 = √3
2. Remembering the Value:
- The most direct way is simply to memorize the value. Knowing that
tan 60° = √3 ≈ 1.732is helpful for quick calculations.
3. Understanding Radians:
- 60 degrees is equal to π/3 radians (approximately 1.047 radians). Therefore,
tan 60° = tan (π/3) = √3. Understanding the relationship between degrees and radians is crucial in trigonometry.
Summary:
The value of tan 60 degrees is √3, which is approximately 1.732. You can determine this value by understanding the side ratios of a 30-60-90 triangle, remembering the value, or converting degrees to radians.
