Answer
The measure of length \[x\] is \[39\text{ units}\].
Work Step by Step
The trigonometric ratio for \[\text{Tangent }A\] will be determined by dividing the opposite side of angle A with the adjacent side of the triangle.
To determine the length of \[x\], first compute the length of \[BC\] using the equation as shown below:
In\[\vartriangle ABD\], we have
\[\begin{align}
& \text{Tangent }A=\frac{\text{Opposite side of angle }A}{\text{Adjacent side of angle }A} \\
& =\frac{BD}{AD} \\
& \text{Tangent 28}{}^\circ =\frac{BD}{600}
\end{align}\]
\[\begin{align}
& BD=\text{Tangent 28}{}^\circ \times 600 \\
& =0.532\times 600 \\
& =319
\end{align}\]
Now, compute the length of the \[CD\] using the equation as shown below:
In\[\vartriangle \text{ACD}\], we have
\[\begin{align}
& \text{Tangent }A=\frac{\text{Opposite side of angle }A}{\text{Adjacent side of angle }A} \\
& =\frac{CD}{AD} \\
& \text{Tangent 25}{}^\circ =\frac{CD}{600}
\end{align}\]
\[\begin{align}
& CD=\text{Tangent 25}{}^\circ \times 600 \\
& =0.4665\times 100 \\
& =280
\end{align}\]
Now, as per the given figure
\[\begin{align}
& x=BC \\
& =BD-CD \\
& =319-280 \\
& =39
\end{align}\]
Hence, the measure of length \[x\] is \[39\text{ units}\].