Question

Can someone please help me.

Answer 1

Option A: $\frac{A B}{A C}$ is equal to Sin C

Option D: $\frac{D E}{D F}$ is equal to Sin C

Explanation:

Given that the triangles ABC and DEF are right triangles.

The triangle ABC is similar to triangle DEF

Since, the triangles are similar, then their ratios of the sides are proportional.

We need to determine the ratios which are equal to Sin C

The value of Sin C can be determined using the trigonometric ratios.

The ratio of Sin C in triangle ABC:

Let us consider the triangle ABC.

$Sin \ C = \frac{opp}{hyp}$

where opp = AB and hyp = AC

Substituting the values, we get;

$Sin C=\frac{AB}{AC}$

Thus, the ratio of Sin C is $\frac{A B}{A C}$

Hence, Option A is the correct answer.

The ratio of Sin C in triangle DEF:

Let us consider the triangle DEF.

Since, the triangles are similar, then their sides and angles are proportional.

Thus, ∠C = ∠F

$Sin \ C = \frac{opp}{hyp}$

where opp = DE and hyp = DF

Substituting the values, we get;

$Sin \ C= \frac{DE}{DF}$

Thus, the ratio of Sin C is $\frac{D E}{D F}$

Hence, Option D is the correct answer.