Answer:
[tex]\tan(22.6)=\frac{a}{12}[/tex]
Step-by-step explanation:
We know that [tex]\cos(22.6)=\frac{b}{13}[/tex]. Rounding the value of b as asked in the problem gives b=12.
From the right-triangle definition of cosine, b must be the adjacent side to the angle 22.6º and the hypothenuse of the triangle must be 3.
Then, a is the opposite side of the angle 22.6º therefore using the definition of sine, [tex]\sin(22.6)=\frac{a}{3}[/tex]. Solving for a, we obtain [tex]a=3 sin(22.6)=3\cos(22.6)\tan(22.6)=b\tan (22.6)=12\tan(22.6)[/tex].
We conclude that [tex]\tan(22.6)=\frac{a}{12}[/tex].
