Answer
Two angles of the large triangle have equal measurement with that of the small triangle. Since, one angle pair is given to have the same measure (right angles). Another angle pair consist of vertical angles with the same measure.
Therefore, the triangles are identical and their corresponding sides are in proportion. Hence, length, \[x=16\text{ in}\text{.}\]
Work Step by Step
The figure shows that the large triangle and the small triangle both contain \[{{90}^{\circ }}\]angles. The other two angles form a pair of vertically opposite angles with equal measurement. Thus, two angles of the large triangle have equal measurement with that of the small triangle. Since, one angle pair is given to have the same measure (right angles). Another angle pair consist of vertical angles with the same measure.
Therefore, the triangles are identical and their corresponding sides are in proportion.
The side with 12 in. is the perpendicular in small triangle and \[x\]is perpendicular in large triangle. The base is 15 in. small triangle and 20 in. in large triangle.
Compute the value of\[x\]as shown below:
\[\begin{align}
& \frac{12}{x}=\frac{15}{20} \\
& 15x=12\times 20 \\
& 15x=240 \\
& x=16
\end{align}\]
Hence, two angles of the large triangle have equal measurement with that of the small triangle. Since, one angle pair is given to have the same measure (right angles). Another angle pair consist of vertical angles with the same measure.
Therefore, the triangles are identical and their corresponding sides are in proportion. Hence, length, \[x=16\text{ in}\text{.}\]
