Answer
$x = 17$ and $y= 15$
Work Step by Step
1. Find the angles in $\bigtriangleup DBC$
$\angle BDC = 55˚$ (Given)
$\angle DCB = 90˚$ (Right angle triangle)
$\angle CBD = 180 - (55 + 90)$
$= 180 - 145$
$= 35˚$
2. Find the angles in $\bigtriangleup ADB$
$\angle A = 38˚$
$\angle ADB = 180 - 55$
$= 125˚$
$\angle DBA = 180 - (125 + 38)$
$= 180 - 163$
$= 17˚$
3. Find $y$
$\frac{y}{sin(\angle DBA)} = \frac{41}{sin(\angle ADB)}$
$\frac{y}{sin(17)} = \frac{41}{sin(125)}$
$y = \frac{41sin(17)}{sin(125)}$
by GDC / calculator
$y = 14.6337$ units
$y = 15$ units
4. Find $x$
$\frac{x}{sin(\angle CBD)} = \frac{DB}{sin(90)}$
$\frac{x}{sin(\angle CBD)} = \frac{29}{1}$
$\frac{x}{sin(35)} = 29$
$x = 29sin(35)$
by GDC / calculator
$x = 16.6337...$ units
$x = 17$ units
Therefore, $x = 17$ and $y= 15$
