Answer:
[tex]2\frac{13}{28}[/tex] feet.
Step-by-step explanation:
We have been given that a 28 feet tree casts a shadow that is 11 1/2 feet long. Kurt is 6 feet tall. We are asked to find length of his shadow.
We will use proportions to solve our given problem.
[tex]\frac{\text{Shadow}}{\text{Actual length}}=\frac{11\frac{1}{2}}{28}[/tex]
[tex]\frac{\text{Shadow}}{\text{Actual length}}=\frac{\frac{23}{2}}{28}[/tex]
[tex]\frac{\text{Shadow}}{\text{Actual length}}=\frac{23}{28*2}[/tex]
[tex]\frac{\text{Shadow}}{\text{Actual length}}=\frac{23}{56}[/tex]
Substitute Kurt's actual height.
[tex]\frac{\text{Shadow}}{6}=\frac{23}{56}[/tex]
[tex]\frac{\text{Shadow}}{6}*6=\frac{23}{56}*6[/tex]
[tex]\text{Shadow}=\frac{23}{28}*3[/tex]
[tex]\text{Shadow}=\frac{69}{28}[/tex]
[tex]\text{Shadow}=2\frac{13}{28}[/tex]
Therefore, Kurt's shadow is [tex]2\frac{13}{28}[/tex] feet.
