The expressions that are equivalent to sin(∠B) are option (B) length of side adjacent to ∠A/length of hypotenuse and option (D) AC/AB are the correct answers.
What is trigonometry?
Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a right-angled triangle and its angles.
For the given situation,
From the diagram,
The right angle is at ∠C, so opposite to that side is hypotenuse.
If we consider angle at ∠B, then the side opposite to that side is opposite side and the other side is adjacent side.
Thus, Sin∠B = [tex]\frac{oppposite}{Hypotenuse}[/tex]
⇒ Sin∠B = [tex]\frac{AC}{AB}[/tex]
From the options, now check which options is equivalent to Sin∠B,
Option (A): tan(∠A)
Now, consider the angle at ∠A,
so, [tex]tan(\angle A)=\frac{oppposite }{adjacent}[/tex]
⇒ [tex]tan(\angle A) =\frac{CB}{AC}[/tex]
Option A is not equivalent to sin(∠B).
Option (B): length of side adjacent to ∠A/length of hypotenuse
⇒ [tex]\frac{AC}{AB}[/tex]
Option B is equivalent to sin(∠B).
Option C: sin(∠A)
[tex]Sin(\angle A)=\frac{CB}{AB}[/tex]
Option C is not equivalent to sin(∠B).
Option D: AC/AB
Option D is equivalent to sin(∠B).
Hence we can conclude that the expressions that are equivalent to sin(∠B) are option (B) length of side adjacent to ∠A/length of hypotenuse and option (D) AC/AB are the correct answers.
Learn more about trigonometry here
https://brainly.com/question/16965914
#SPJ2
