Question

HELP!!!!!!!!!!!!!! I learned this two years ago and I don't remember how to do this anymore!!!!!!

Answer 1

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 $\alpha$ , 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, $\sin \alpha = \frac{a}{b}$

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, $\cos \alpha = \frac{c}{b}$

C.

Next, it has been established that side c is the adjacent and side a is the opposite side. Using this info, $\tan \alpha = \frac{a}{c}$