h= 22.6, CT =47º, CA=15.4
1) We're going to use trig ratios for that. So to find CT, the hypotenuse, and considering the angle 43º as our reference, we can write:
[tex]\begin{gathered} \cos (43)=\frac{adjacent}{\text{hypotenuse}} \\ \cos (43)\text{ =}\frac{16.5}{h} \\ \cos (43)h=16.5 \\ h=\frac{16.5}{\cos (43)} \\ h=22.5609\approx22.6 \end{gathered}[/tex]
So the CT is equal approximately to 22.6.
2) Now let's find out the measure of angle C. The simplest way is to consider the fact that every triangle has the sum of its interior angles as 180º
90º +43º + C = 180º
133º + C = 180º
C =180º -133º
C = 47º
3) Let's focus on CA leg.
Concerning that, we can make use of another trig ratio. Since we know the measure of angle C
[tex]\begin{gathered} \tan (47)=\frac{opposite}{\text{adjacent}} \\ \tan (47)\text{ =}\frac{16.5}{CA} \\ CA=\frac{16.5}{\tan (47)} \\ CA\text{ =15.38649}\approx15.4 \end{gathered}[/tex]
CA is approximately 15.4
