Question

Use this picture to answer the question. If the oak tree is 2 feet taller, with the same shadow, and how far would it be from the top of the tree to the far end of the shadow? Round to the nearest 10th if needed.

Answer 1

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

`\begin{gathered} \text{hypotenus}^2=\text{opposite}^2+\text{adjacent}^2 \\ \text{hypotenus}=26ft \\ \text{opposite}=10ft \end{gathered}`

By substituting the values, we will have

`\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}`

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

`\begin{gathered} \text{hypotenus}^2=\text{opposite}^2+\text{adjacent}^2 \\ \text{hypotenus}=y \\ \text{opposite}=12ft \\ \text{adjacent}=24ft \end{gathered}`
`\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}`

Hence,

The final answer = 26.8ft