In a right-angled triangle, the sine of an angle is the length of the opposite side, divided by the length of the triangle's hypotenuse. Depending upon the quadrants, the sine function can have both positive as well as negative values. Sine has a positive value in the first and second quadrant whereas sine has a negative value in the third and fourth quadrant. Sine formula is used to find the angle if the perpendicular and hypotenuse of the right-angled triangle is known to us. The sine formula is explained below.
What Is the Sine formula?
The sine function of a right triangle is the ratio of its perpendicular to its height. Thus, sine formula can be expressed as,
sin θ = P/H
P = perpendicular
H = hypotenuse
Let us see the applications of sine formula in the below solved examples.
Solved Examples Using Sine formula
Example 1: Find the side of a right-angle triangle whose hypotenuse is 14 units and the angle opposite the side is 30 degrees.
To find: Side (P)
θ = 30 degree
H = 14 cm
Using the sine formula,
sinθ = P/H
sin30 = P/14
0.5 = P/14
P = 0.5(14)
P = 7
Answer: The Perpendicular side of a right-angle triangle is 7 Units.
Example 2: Find sin θ using the sine formula if Hypotenuse = 4.9 units, the base side of the angle = 4 units, and perpendicular = 2.8 degrees.