Answer:
C
Step-by-step explanation:
Remember the mnemonic: SohCahToa, where:
[tex]\sin(\theta)=\text{opposite}/\text{hypotenuse}\\\cos(\theta)=\text{adjacent}/\text{hypotenuse}\\\tan(\theta)=\text{opposite}/\text{adjacent}[/tex]
Let's determine our side lengths first.
Note that our angle is A. So, we have to determine the sides with respect to A.
The opposite side to A is 16.
The adjacent side is 12.
And the hypotenuse is 20.
With this, we can find our trig ratios:
Sine:
[tex]\sin(A)=\text{opp}/\text{hyp}[/tex]
Substitute 16 for the opposite and 20 for the hypotenuse. This yields:
[tex]\sin(A)=16/20[/tex]
Reduce:
[tex]\sin(A)=4/5[/tex]
Cosine:
[tex]\cos(A)=\text{adj}/\text{hyp}[/tex]
Substitute 12 for the adjacent and 20 for the hypotenuse. This yields:
[tex]\cos(A)=12/20[/tex]
Reduce:
[tex]\cos(A)=3/5[/tex]
Tangent:
[tex]\tan(A)=\text{opp}/\text{adj}[/tex]
Substitute 16 for the opposite and 12 for the adjacent. This yields:
[tex]\tan(A)=16/12[/tex]
Reduce:
[tex]\tan(A)=4/3[/tex]
So, our answers are:
[tex]\frac{4}{5}, \frac{3}{5}, \text{ and } \frac{4}{3}[/tex]
Out of the answer choices, the choice that represents this is C.
So, our correct answer is C.
And we're done!
