The equations of trigonometric ratios are true for options (B), (C), (E), (F) is the correct answer.
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 triangle (right-angled triangle) and its angles.
For the given situation,
The diagram shows the right triangle ABC and the angle at ∠A = 48°, ∠c = 90° and the side measures of triangle.
Sum of angles of triangle = 180°
⇒ [tex]\angle A +\angle B+\angle C=180[/tex]
⇒ [tex]\angle B=180-90-48[/tex]
⇒ [tex]\angle B=42[/tex]
The side opposite to right angle is hypotenuse side.
The side opposite to angle θ is opposite side and
the other side is adjacent side.
The trigonometric ratios are
[tex]sin \theta =\frac{opposite}{hypotenuse}[/tex], [tex]cos\theta=\frac{adjacent}{hypotenuse}[/tex], [tex]tan \theta=\frac{opposite }{adjacent}[/tex]
Option A:
[tex]cos42=\frac{a}{c}[/tex]
So, option A is false.
Option B:
[tex]cos48=\frac{b}{c}[/tex]
So, option B is true.
Option C:
[tex]sin 42 =\frac{b}{c}[/tex]
So, option C is true.
Option D:
[tex]sin 48 =\frac{a}{c}[/tex]
So, option D is false.
Option E:
[tex]tan42=\frac{ b}{a}[/tex]
So, option E is true.
Option F:
[tex]tan48=\frac{ a}{b}[/tex]
So, option F is true.
Hence we can conclude that the equations of trigonometric ratios are true for options (B), (C), (E), (F) is the correct answer.
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