Answer
The ratio of the side opposite to the acute angle to the hypotenuse of the right triangle is called the sine of an acute angle of a right triangle. The ratio of the side next to the angle and the hypotenuse of the right triangle is known as the cosine of an acute angle of a right triangle.
Work Step by Step
The longest side of the right triangle is known as the hypotenuse. There is an acute angle and a right angle in right angle triangle. The both legs of the triangle are related to an acute angle. One leg is known as the side opposite to the acute angle and another leg is side adjacent to the acute angle.
Example:
The lengths of the right angle triangle are 3cm in height, 4cm in base, and 5cm hypotenuse. It is required to define the similarity and the difference between the sine and the cosine ratio.
The difference between the sine ratio and cosine ratio is that the ratio of the side opposite to the acute angle to the hypotenuse of the right triangle is called the sine of an acute angle of a right triangle. The ratio of the side next to the angle and the hypotenuse of the right triangle is known as the cosine of an acute angle of a right triangle.
.
In the given data, the height of the right triangle is 3 cm, the base is 4cm and the hypotenuse is 5 cm. The sine of an acute angle is\[\sin \theta =\frac{3}{5}\]. The cosine ratio of an acute angle is\[\cos \theta =\frac{4}{5}\].
The similarity between the sine and cosine ratio of a right triangle is that they both are known as co-functions, because sine or cosine ratio of an acute angle is equivalent to its co-function of the complement of the angle.
Hence, the sine of the acute angle of a right triangle is\[\frac{3}{5}\], the cosine ratio of an acute angle is\[\cos \theta =\frac{4}{5}\].
