Answer:
[tex]\sf \tan B=0.34[/tex]
[tex]\sf \cos B=0.95[/tex]
[tex]\sf \sin B=0.32[/tex]
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
- [tex]\theta[/tex] is the angle
- O is the side opposite the angle
- A is the side adjacent the angle
- H is the hypotenuse (the side opposite the right angle)
If ΔXYZ ~ ΔACB then ∠B = ∠Y
From inspection of ΔXYZ:
- [tex]\theta[/tex] = Y
- O = XZ = 9.6
- A = XY = 28
- H = ZY = 29.6
[tex]\sf \implies \tan B = \tan Y = \dfrac{9.6}{28}=0.34[/tex]
[tex]\sf \implies \cos B = \cos Y = \dfrac{28}{29.6}=0.95[/tex]
[tex]\sf \implies \sin B = \sin Y = \dfrac{9.6}{29.6}=0.32[/tex]
