Question

1. The length of the shadow of the factory chimney is 32.5 m and the length of the shadow of a nearby pole 2.4 m high is 2.72 m. Calculate the height of the chimney.

Answer 1

There is a proportional relation between the actual heights of 2 objects and their shadows at the same time

`(h_1)/(h_2)=(sh_1)/(sh_2)`

Since the shadow of the chimney is 32.5 m, then

`sh_1=32.5`

Since the shadow of the pole is 2.72 m, then

`sh_2=2.72`

Since the height of the pole is 2.4 m, then

`h_2=2.4`

Substitute them in the rule above

`(h_1)/(2.4)=(32.5)/(2.72)`

Use the cross-multiplication

`\begin{gathered} h_1*2.72=2.4*32.5 \\ 2.72h_1=78 \end{gathered}`

Divide both sides by 2.72

`\begin{gathered} (2.72h)/(2.72)=(78)/(2.72) \\ h=28.67647059 \end{gathered}`

Round it to the nearest 2 decimal places

The height of the chimney is 28.68 m