Question

Triangle ABC and DEF are right triangles, as shown. Triangle ABC is similar to triangle DEF. which ratios are equal to sin C?

Answer 1

Answer:

First option and Fourth option.

Step-by-step explanation:

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

$sin\alpha=\frac{opposite}{hypotenuse}$

In this case you know that:

$\alpha =C$

Since triangle ABC is similar to triangle DEF:

$\angle C=\angle F$

Let's begin with the triangle ABC.

You can identify that:

$opposite=AB\\hypotenuse=AC$

Then, substituing values, you get:

$sinC=\frac{AB}{AC}$

In triangle DEF, you know that:

$opposite=DE\\hypotenuse=DF$

So, substituing values, you get:

$sinF=sinC=\frac{DE}{DF}$