Find the remaining sides and angles. round your answers to the nearest tenth. show your work.

These are all the sides and angles:
a = 3
b = 18.76
c = 19
A = 9.1°
B = 80.9°
C = 90°

Explanation:

As per the usual convention the side c is opposite to the angle C, side a is opposite to angle a, and side b is opposite to angle B.

That means that c is the hypotenuse of the triangle.

Then, a is one leg, and b is the other leg.

Therefore, you can use Pythagorean theorem to find the unknown leg, b:

c² = a² + b² ⇒ b² = c² - a²
⇒ b² = 19² - 3² = 352
⇒ b = √352 = 18.76

Now you can use any trigonometric ratio to find one of the unknowm angles.

I wll use sine ratio to find the angle opposite to a:

sin (A) = a / 19 = 3 / 19 

⇒ A = arcsin (3/19) ≈ 9.1°.

Then, the other angle is: B = 180° - 9.1° - 90° = 80.9°

And those are all the sides and angles:
a = 3
b = 18.76
c = 19
A = 9.1°
B = 80.9°
C = 90°