Respuesta :

luisejr77

Answer:

First option and Fourth option.

Step-by-step explanation:

To solve this exercise you need to use the following Trigonometric Identity:

[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]

In this case you know that:

[tex]\alpha =C[/tex]

Since triangle ABC is similar to triangle DEF:

[tex]\angle C=\angle F[/tex]

Let's begin with the triangle ABC.

You can identify that:

[tex]opposite=AB\\hypotenuse=AC[/tex]

Then, substituing values, you get:

[tex]sinC=\frac{AB}{AC}[/tex]

In triangle DEF, you know that:

[tex]opposite=DE\\hypotenuse=DF[/tex]

So, substituing values, you get:

[tex]sinF=sinC=\frac{DE}{DF}[/tex]

The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. The correct answers are first and fourth.

What is Sine (Sinθ)?

The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,

Sin(θ) = Perpendicular/Hypotenuse

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The hypotenuse is the longest side of the triangle.

What are Similar Figures?

Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".

Two triangles are told to be similar triangles if the ratio of their corresponding sides is in equal ratio. Therefore, the value of sin C can be written as,

Sin C = AB/AC = DE/ DF

Hence, the correct answers are first and fourth.

Learn more about Sine:

https://brainly.com/question/21286835

#SPJ5