Answer:
39 feet
Step-by-step explanation:
In the attached diagram
The height of the tree = AB
The height of the man =DE
The length of the shadow =BC
We want to determine how far away from the tree the person is, i.e. |AD|=y
In Triangle ABC
[tex]Tan \theta=\dfrac{32}{48}[/tex]
In Triangle CED
[tex]Tan \theta=\dfrac{6}{48-y}[/tex]
Therefore:
[tex]Tan \theta=\dfrac{32}{48}=\dfrac{6}{48-y}\\\dfrac{32}{48}=\dfrac{6}{48-y}\\$Cross Multiply\\32(48-y)=48*6\\1536-32y=288\\32y=1536-288\\32y=1248\\Divide both sides by 32\\y=39[/tex]
Therefore, the distance of the man from the tree is 39 feet.
