Options (1), (4) and (5) are the correct options.
Trigonometric ratios of an angle in a right triangle:
- Trigonometric ratios of an angle in a right triangle are,
[tex]\text{sin}\theta=\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
[tex]\text{cos}\theta=\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]\text{tan}\theta=\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
From the picture attached,
- ΔABC is a right triangle.
- AB = 27, BC = 36 and AC = 45
Substitute the values in the ratios,
[tex]\text{sin}A=\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
[tex]\text{sin}A=\frac{\text{BC}}{\text{AC}}[/tex]
[tex]\text{sin}A=\frac{\text{36}}{\text{45}}[/tex]
[tex]\text{cos}A=\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]\text{cos}A=\frac{\text{AB}}{\text{AC}}[/tex]
[tex]\text{cos}A=\frac{\text{27}}{\text{45}}[/tex]
[tex]\text{tan}\theta=\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
[tex]\text{tan}A=\frac{\text{BC}}{\text{AB}}[/tex]
[tex]\text{tan}A=\frac{36}{27}[/tex]
Therefore, Options (1), (4) and (5) are the correct options.
Learn more about the trigonometric ratios here,
https://brainly.com/question/1592477?referrer=searchResults
