The shadow cast by a one-foot ruler is 8 inches long. At the same time the shadow cast by a pine tree is 24 feet long. What is the height in feet of the pine tree

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.

${teks-lihat-gambar} Abdulazeez10

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