The problem involves solving for side $b$, and angles $A$ and $B$ in a right triangle where:

1. $a = 6$, $c = 19$ (hypotenuse).
2. We need to round to four decimal places.

Step 1: Solve for $b$ using the Pythagorean theorem

$a^2 + b^2 = c^2$ Substitute the given values: $6^2 + b^2 = 19^2$ $36 + b^2 = 361$ $b^2 = 361 - 36 = 325$ $b = \sqrt{325} \approx 18.0278$

Step 2: Solve for angles $A$ and $B$

Use trigonometric ratios:

• (\sin(A