Answer:
[tex]\approx10.29\text{ feet}[/tex]
Step-by-step explanation:
Please refer to the attachment.
By AA Similarity, the two triangles are similar.
Therefore, corresponding parts of them are proportional.
Therefore, we can write the following proportion:
[tex]\frac{7}{24}=\frac{3}{x+3}[/tex]
We will solve for x. Cross-multiply:
[tex]7(x+3)=24(3)[/tex]
Distribute:
[tex]7x+21=72[/tex]
Subtract 21 from both sides:
[tex]7x=51[/tex]
Divide both sides by 7. So, the value of x is:
[tex]x\approx7.2857[/tex]
However, that is only the value of x.
The shadow of the tree is (x+3).
Hence, we will need tot add 3 to our value. Therefore, the actual length of the shadow of the tree is approximately:
[tex]\approx10.2857\approx10.29\text{ feet}[/tex]
