Trigonometric Ratios are the relationship between an angle and the three sides of a right angled triangle.

The ratio of the opposite side to the hypotenuse is the sine of the angle, shortened to sin. The opposite side is the side opposite the angle.

`sin(x) = frac(text(Opposite))(text(Hypotenuse))`

If an angle and one length (hypotenuse or opposite) are known, find the sin value for that angle using a calculator (or tables).

If the two lengths (hypotenuse and opposite) are known, the formula gives the sin of the angle. Using a calculator, look up the value of the angle using the inverse operation (which is written as sin-1).


1. What is the length of AB?

Answer: 7.053 cm

sin x = `frac(text(opposite))(text(hypotenuse))`

sin 36 = `frac(text(AB))(12)`

0.5878 x 12 = AB, therefore AB = 7.053

2. What is the value of the angle x?

Answer: 34.2º

sin x = `frac(text(opposite))(text(hypotenuse))`

sin x = `frac(9)(16)`

sin x = 0.5625

x = sin-1 0.5625; therefore x = 34.23º