Answer
The height of tree is\[16\text{ feet}\].
Work Step by Step
The figure shows that the large triangle with the tree on the right-hand side and the small triangle with the vertical rod on the right-hand side both contains\[{{90}^{\circ }}\]angles. The angle that is formed by sun rays is equal in both the triangles.
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 are proportional.
The figure shows that the height of vertical is 8 feet and length of its shadow is 6 feet. It also shows that the length of the shadow of tree is 12 feet.
Let height of tree be\[x\]feet and\[x\] is the height of tree and is opposite to the \[{{90}^{\circ }}\]angle in large triangle. 8 ft. is the height of vertical rod and is opposite to the \[{{90}^{\circ }}\]angle in small triangle. The shadow of tree is 12 feet in large triangle and the shadow of vertical rod is 6 feet in the small triangle. opposite
Thus, \[\frac{x}{8}=\frac{12}{6}\]
Compute \[x\]by applying the cross-multiplication principle for proportion, which states that if\[\begin{align}
& \frac{a}{b}=\frac{c}{d} \\
& ad=bc
\end{align}\]
So, apply the cross-product principle as shown below:
\[6x=12.8\]
Multiply 12 and 8 which is equal to 96 as shown below:
\[6x=96\]
Divide both sides by 6 to compute value of\[x\]as shown below:
\[\begin{align}
& \frac{6x}{6}=\frac{96}{6} \\
& x=16
\end{align}\]
