Answer :
Answer:
The height in feet of the pine tree is 36 feet
Step-by-step explanation:
Please see the attachment below for an illustrative diagram.
In the diagram,
/AB/ represents the height of the pine tree
/BD/ represents the length of the shadow cast by the pine tree
/EC/ represents the length of the ruler ( one foot)
/CD/ represents the length of the shadow cast by the one-foot ruler
Consider triangle ADB and triangle EDC
Triangles ADB and EDC are similar triangles.
Hence, we can write that
[tex]\frac{/AB/}{/EC/} = \frac{/BD/}{/CD/}[/tex]
/AB/ = ??
/EC/ = 1 ft
/BD/ = 24 ft
/CD/ = 8 inches
First we will convert 8 inches to feet
Since, 12 inches = 1 foot
Then, 8 inches = [tex]x[/tex]
[tex]x = \frac{8}{12} \\[/tex] ft
[tex]x = \frac{2}{3}\\[/tex] ft
Hence.
/CD/ = [tex]\frac{2}{3}[/tex] ft
Now, putting the values into
[tex]\frac{/AB/}{/EC/} = \frac{/BD/}{/CD/}[/tex]
[tex]\frac{/AB/}{1} = \frac{/24/}{/\frac{2}{3} /}[/tex]
[tex]/AB/= \frac{/24/}{/\frac{2}{3} /}\\[/tex]
[tex]/AB/ = 36[/tex] ft
Hence, the height in feet of the pine tree is 36 feet.
