Sin

# Sin

GCSE(F), GCSE(H),

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).

## Examples

1. What is the length of AB?

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?

sin x = frac(text(opposite))(text(hypotenuse))
sin x = frac(9)(16)