Answer
Two angles of the large triangle have equal measurement with that of the small triangle. Therefore, the triangles are identical and their corresponding sides are proportional. Hence, \[x=6\text{ ft}\text{.}\]
Work Step by Step
The figure shows that the large triangle and the small triangle both contain equal angles marked with one tick. 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. Therefore, the triangles are identical and their corresponding sides in proportion.
The side with 5 ft. is the side of small triangle corresponding to the 7.5 ft. which is the side of large triangle. The side with 4 ft. and \[x\] are opposite to the vertically opposite angles in small triangle and large triangle, respectively. The base is 15 in. small triangle and 20 in. in large triangle.
Compute the value of\[x\]as shown below:
\[\begin{align}
& \frac{5}{7.5}=\frac{4}{x} \\
& 5x=7.5\times 4 \\
& 5x=30 \\
& x=6
\end{align}\]
Hence, two angles of the large triangle have equal measurement with that of the small triangle. Therefore, the triangles are identical and their corresponding sides are in proportion. Hence, \[x=6\text{ ft}\text{.}\]
