Adjacent Vs Opposite: Understanding the Difference Between these Terms
When it comes to mathematics, geometry and trigonometry, there are various terms that we use to describe different concepts. Many times, these terms may sound similar or may be confusing to understand. Two such terms are adjacent and opposite. In this article, we will understand the meanings of these terms and their differences.
Adjacent: In most cases, adjacent means ‘next to’ or ‘beside.’ In the context of geometry and trigonometry, the term adjacent is used to refer to two sides of a right-angle triangle that are connected to the angle. It is essential to note that the adjacent sides of a triangle always form the angle where the value of an angle is measured. Therefore, if we have a triangle with angles A, B, and C, and angle C is the right angle, sides AB and BC are adjacent.
Opposite: The term opposite refers to that which is located across from something or someone or on the other side. In the context of geometry and trigonometry, the term opposite is used to refer to the side of a right-angle triangle that is positioned opposite to the angle. This means that the side is not touching the angle, but it is positioned opposite to it. Thus, for a triangle with angles A, B, and C, the opposite side of angle C is AB.
Understanding the difference between Adjacent and Opposite
To better understand the difference between adjacent and opposite, let us use an example. Suppose we have a right triangle with angles A, B, and C, where angle C is the right angle. If angle B measures 45 degrees, then angle A will also measure 45 degrees because the sum of the angles of a triangle is 180 degrees.
In this case, side AB is opposite to angle C, while side BC is adjacent to angle B. Therefore, we can say that side BC is adjacent to angle B and opposite to angle C. Similarly, side AB is opposite to angle C and adjacent to angle A.
The uses of Adjacent and Opposite in Trigonometry
In trigonometry, the terms adjacent and opposite are used extensively to calculate and solve problems involving right-angle triangles. With the help of these terms, we can calculate the values of trigonometric ratios such as sine, cosine, and tangent.
Trigonometric ratios are the ratios of two sides of a right-angle triangle. The three main trigonometric ratios are sine, cosine, and tangent. These ratios are calculated using the sides of a right-angle triangle, where one angle is 90 degrees.
Sin = opposite/hypotenuse
Cos = adjacent/hypotenuse
Tan = opposite/adjacent
In these ratios, adjacent and opposite are used to refer to the sides that are adjacent and opposite to the angle. Similarly, the hypotenuse is the longest side of a right-angle triangle and is always positioned opposite to the right angle.
Example of the use of Adjacent and Opposite in Trigonometry
Suppose we have a right-angle triangle with an angle of 60 degrees, and the opposite side to this angle is 10cm, and the hypotenuse is 20cm, then we can calculate the values of sine and cosine using the adjacent and opposite sides as follows:
Sin 60 = opposite/hypotenuse
Sin 60 = 10/20
Sin 60 = 0.5
Cos 60 = adjacent/hypotenuse
Cos 60 = 10/20
Cos 60 = 0.5
We can see from the above calculation that the values of sine and cosine are the same, which is expected because in a right-angle triangle with a 60-degree angle, the adjacent and opposite sides are equal.
Conclusion
In summary, adjacent and opposite are two essential terms in mathematics and trigonometry. Adjacent refers to the side next to or beside something, while opposite refers to the side across from something or someone or on the other side. In trigonometry, adjacent and opposite are used extensively to calculate trigonometric ratios such as sine, cosine, and tangent. These ratios are calculated using the adjacent and opposite sides of a right-angle triangle. Therefore, understanding the difference between adjacent and opposite is essential to excel in geometry, trigonometry, and other mathematical disciplines.