Trigonometry Opposite Adjacent

What is Trigonometry?

Trigonometry is a branch of mathematics which deals with the relation between different angles and sides of a triangle. Basically trigonometry deals with a right triangle. Different trigonometric ratios are defined with respect to the two acute angles in the right triangle. Consider the right triangle ABC given below with angle B as right angle.

Right Triangle

We can define trigonometric ratio taking any of the angles A and C into consideration. Let us first try to define these ratios, taking angle C as θ. The most important thing to note down is that:

Side opposite to right angle is called hypotenuse (H)

Side opposite to the acute angle in consideration (θ) is called perpendicular (P)

Side adjacent to the acute angle in consideration (θ) is called base (B)

Here in the given triangle AC is hypotenuse, AB is altitude and BC is base.

 

How to we define trigonometric ratios using opposite and adjacent sides

 

Now, you might have a clear picture of all three sides a triangle. Let us now try to understand different trigonometric ratios.

Sine Ratio: Abbreviated as sin, is defined as the ratio of perpendicular to hypotenuse.

Cosine Ratio: Abbreviated as cos, is defined as the ratio of base to hypotenuse.

Tangent Ratio: Abbreviated as tan, is defined as the ratio of perpendicular to base.

So we conclude that sine ratio involves the opposite and hypotenuse whereas cosine ratio involves the adjacent and hypotenuse. Tangent ratio involves the opposite and adjacent sides of the triangle.

 

Examples of Trigonometry Opposite Adjacent

 

1.            Name the opposite and adjacent sides for θ in the triangle shown below.

Right Triangle

Solution:

                The opposite side is PQ and adjacent side is QR.

2.            Define trigonometric ratios for angle R in triangle shown below.

Right Triangle

Solution:

The trigonometric ratios are: