So remember the acronym "SOH CAH TOA"
- Sin = Opposite/Hypotenuse
- Cos = Adjacent/Hypotenuse
- Tan = Opposite/Adjacent
- Opposite = Side that doesn't touch the angle
- Adjacent = Side that touches the angle
- Hypotenuse = Side that is across from the right angle
A.
So we see that side a doesn't touch angle [tex]\alpha[/tex] , hence making it the opposite side. And we see that side b is across from the right angle, making it the hypotenuse. Using this info, [tex]\sin \alpha = \frac{a}{b}[/tex]
B.
So we already know from part A that side b is the hypotenuse. And also since side c touches the angle, it is the adjacent. Using this info, [tex]\cos \alpha = \frac{c}{b}[/tex]
C.
Next, it has been established that side c is the adjacent and side a is the opposite side. Using this info, [tex]\tan \alpha = \frac{a}{c}[/tex]
