Answer:
[tex]\displaystyle \sin\theta=\frac{4}{5}[/tex]
Step-by-step 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
[tex]\displaystyle \sin\theta=\frac{\text{opposite leg}}{\text{hypotenuse}}[/tex]
Let's focus on the angle θ. Its opposite leg is 8 cm and the hypotenuse is 10 cm, thus:
[tex]\displaystyle \sin\theta=\frac{8}{10}[/tex]
Simplifying:
[tex]\boxed{\displaystyle \sin\theta=\frac{4}{5}}[/tex]
