Question

Find the value of sin 0 in each of the following figures.​

Answer 1

`\displaystyle \sin\theta=(4)/(5)`

Explanation:

Trigonometric Ratios

The ratios of the sides of a right triangle are called trigonometric ratios.

The longest side of a right triangle is called the hypotenuse and the other two sides are the legs.

Selecting any of the acute angles as a reference, we identify an adjacent leg and an opposite leg. The trigonometric ratios are defined upon those sides.

Sine Ratio

`\displaystyle \sin\theta=\frac{\text{opposite leg}}{\text{hypotenuse}}`

Let's focus on the angle θ. Its opposite leg is 8 cm and the hypotenuse is 10 cm, thus:

`\displaystyle \sin\theta=(8)/(10)`

Simplifying:

`\boxed{\displaystyle \sin\theta=(4)/(5)}`