Answer
$x = 84.7~m$
Work Step by Step
We can convert the angle $30^{\circ}50'$ to degrees:
$\theta = 30^{\circ}50' = (30+\frac{50}{60})^{\circ} = 30.8^{\circ}$
We can find the length $d$ of the line in the middle:
$\frac{198.4~m}{d} = cos~\theta$
$d = \frac{198.4~m}{cos(30.8^{\circ})}$
$d = 231.0~m$
The angle opposite $x$ is $21^{\circ}30'$. We can convert this angle to degrees:
$21^{\circ}30' = (21+\frac{30}{60})^{\circ} = 21.5^{\circ}$
We can find the length of $x$:
$\frac{x}{d} = sin(21.5^{\circ})$
$x = d~sin(21.5^{\circ})$
$x = (231.0~m)~sin(21.5^{\circ})$
$x = 84.7~m$
