Answer
The ratio of the side opposite to the acute angle to the hypotenuse of the right triangle is known as the sine 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 two legs of the triangle are related to an acute angle. One leg is known as a side opposite to the acute angle and another leg is side next to the acute angle.
Example:
The lengths of the right angle triangle are 3cm high, 4cm base,and 5cm hypotenuse.It is required to compute the sine of acute angles of a right angled triangle.Sine of an acute angle of a right triangle is the ratio of the side, which is opposite to the acute angle to the hypotenuse of the right triangle.
In the given data, the height of the right triangle is 3 cm, base is 4cm and the hypotenuse is 5cm.The sine of acute angle is\[\sin \theta =\frac{3}{5}\].
Hence, the sine of acute angle of right triangle is\[\frac{3}{5}\].
