In trigonometry, the "opposite" refers to the side of a right-angled triangle that is directly across from the angle you are considering (excluding the right angle).
Understanding Opposite, Adjacent, and Hypotenuse
To understand "opposite," it's crucial to identify all three sides of a right-angled triangle relative to a specific acute angle (an angle less than 90 degrees):
- Hypotenuse: The longest side of the right-angled triangle, always opposite the right angle (90 degrees).
- Opposite: The side directly across from the angle you are referencing.
- Adjacent: The side that is next to the angle you are referencing (and is not the hypotenuse).
Visual Representation
Imagine a right-angled triangle ABC, where angle B is the right angle.
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If you are considering angle A:
- The hypotenuse is AC.
- The opposite side is BC.
- The adjacent side is AB.
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If you are considering angle C:
- The hypotenuse is AC.
- The opposite side is AB.
- The adjacent side is BC.
Importance in Trigonometric Ratios
The "opposite" side is critical for calculating trigonometric ratios such as sine (sin), cosine (cos), and tangent (tan):
- Sine (sin) = Opposite / Hypotenuse
- Cosine (cos) = Adjacent / Hypotenuse
- Tangent (tan) = Opposite / Adjacent
Example
Let's say in right-angled triangle ABC (angle B = 90 degrees), angle A is 30 degrees, the hypotenuse AC is 10 units, and side BC (opposite to angle A) is 5 units.
- sin(30°) = Opposite / Hypotenuse = 5 / 10 = 0.5
Conclusion
The "opposite" side in trigonometry is the side of a right triangle located directly across from the reference angle and is essential for defining the trigonometric ratios.
