Trigonometric Ratio: Sine

Trigonometric Ratio: Sine

How to solve sine (trigonometric ratio) problems: definition, examples, and their solutions.

Definition

sin A = (Opposite side) / (Hypotenuse). Remember: SOH (Sine, Opposite, and Hypotenuse).

Sine is the ratio of a right triangle's
(Opposite side) / (Hypotenuse).

SOH:
Sine = (Opposite) / (Hypotenuse)

Trigonometric ratios can be used
to express the shape of a triangle.

Instead of drawing the picture
or writing all the sides and angles of a triangle,
you can write 'sin A = '
to show the ratio of (opposite side)/(hypotenuse),
which shows the shape of a triangle.

Example 1

Find sin A. Hypotenuse: 5, The side opposite to angle A: 3, The side adjacent to angle A: 4.

Sine: SOH.
So sin A = (Opposite side, 3) / (Hypotenuse, 5).

Example 2

Find sin A. Hypotenuse: 13, The side opposite to angle A: 12, The side adjacent to angle A: 5.

Sine: SOH.
So sin A = (Opposite side, 12) / (Hypotenuse, 13).

Example 3

If sin A = 4/5, find the value of x. Hypotenuse: 10, The side opposite to angle A: x.

Sine: SOH.
So sin A = (Opposite side, x) / (Hypotenuse, 10) = 4/5.