Question

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 1

The height in feet of the pine tree is 36 feet

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

`(/AB/)/(/EC/) = (/BD/)/(/CD/)`

/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 =
`x`

`x = (8)/(12) \\` ft

`x = (2)/(3)\\` ft

Hence.

/CD/ =
`(2)/(3)` ft

Now, putting the values into

`(/AB/)/(/EC/) = (/BD/)/(/CD/)`

`(/AB/)/(1) = (/24/)/(/(2)/(3) /)`

`/AB/= (/24/)/(/(2)/(3) /)\\`

`/AB/ = 36` ft

Hence, the height in feet of the pine tree is 36 feet.