Answer:
Step 1:
Figure out the length of the shadow when the height of the oak tree is 10ft
We will use the Pythagoras theorem below
[tex]\begin{gathered} \text{hypotenus}^2=\text{opposite}^2+\text{adjacent}^2 \\ \text{hypotenus}=26ft \\ \text{opposite}=10ft \end{gathered}[/tex]
By substituting the values, we will have
[tex]\begin{gathered} \text{hypotenus}^2=\text{opposite}^2+\text{adjacent}^2 \\ 26^2=10^2+x^2 \\ 676=100+x^2 \\ x^2=676-100 \\ x^2=576 \\ x=\sqrt[]{576} \\ x=24ft \end{gathered}[/tex]
Step 2:
We will calculate the length from the top of the tree to the end of the shadow
We will use the Pythagoras theorem below
[tex]\begin{gathered} \text{hypotenus}^2=\text{opposite}^2+\text{adjacent}^2 \\ \text{hypotenus}=y \\ \text{opposite}=12ft \\ \text{adjacent}=24ft \end{gathered}[/tex][tex]\begin{gathered} \text{hypotenus}^2=\text{opposite}^2+\text{adjacent}^2 \\ y^2=12^2+24^2 \\ y^2=144+576 \\ y^2=720 \\ y=\sqrt[]{720} \\ y=26.8ft \end{gathered}[/tex]
Hence,
The final answer = 26.8ft
