Answer
The measure of length x is \[50\text{ units}\].
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\[\vartriangle ABC\], we have
\[\begin{align}
& \text{Tangent }A=\frac{\text{Opposite side of angle }A}{\text{Adjacent side of angle }A} \\
& =\frac{BC}{AC} \\
& \text{Tangent 20}{}^\circ =\frac{BC}{100}
\end{align}\]
\[\begin{align}
& BC=\text{Tangent 20}{}^\circ \times 100 \\
& =0.3641\times 100 \\
& =36.41
\end{align}\]
Now, compute the length of the \[CD\] using the equation as shown below:
In\[\vartriangle ACD\], we have
\[\begin{align}
& \text{Tangent }A=\frac{\text{Opposite side of angle }A}{\text{Adjacent side of angle }A} \\
& =\frac{CD}{AC} \\
& \text{Tangent 8}{}^\circ =\frac{CD}{100}
\end{align}\]
\[\begin{align}
& CD=\text{Tangent 8}{}^\circ \times 100 \\
& =0.1405\times 100 \\
& =14
\end{align}\]
Now, as per the given figure
\[\begin{align}
& x=BD \\
& =BC+CD \\
& =36+14 \\
& =50
\end{align}\]
Hence, the measure of length x is \[50\text{ units}\].
