In the given figure :
Angle A = 16 degrees
Length AB = 20
AC = x, BC = y
Apply the trignometric ratio of sin 16
Trignometric ratio of sine is epxress as :
[tex]\text{ }\sin \theta=\frac{Perpendicular}{Hypotenuse}[/tex]for angle =16, substitute the value of perpendicular BC =y, AB = 20
[tex]\begin{gathered} \text{ }\sin \theta=\frac{Perpendicular}{Hypotenuse} \\ \sin 16=\frac{BC}{AB} \\ \sin 16=\frac{y}{20} \\ y=20\text{ }\sin 16 \\ y=20(0.275) \\ y=5.5 \end{gathered}[/tex]Thus, we get BC = 5.5
Similarly Apply the trignometric ratio of Cosine 16
Trignometric ratio of cosine is express as:
[tex]\cos \theta=\frac{Base}{Hypotenuse}[/tex]For angle = 16
[tex]\begin{gathered} \cos \theta=\frac{Base}{Hypotenuse} \\ \cos 16=\frac{AC}{AB} \\ \cos 16=\frac{x}{20} \\ x=20(\text{cos}16) \\ x=20(0.961) \\ x=19.22 \end{gathered}[/tex]AC = 19.22
Answer : BC = 5.5, AC = 19.22
