Question

A tree casts a shadow 35m long. At the same time, a sign post casts ashadow 7m long. The sign post is 4.5 m tall. How tall is the tree?

Answer 1

It is given that a tree casts 35m long shadow and at the same time a pole casts a shadow 7m tall.The pole is 4.5m tall.

So make 2 similar triangles as follows:

As both shadows are cast at the same time, the angle is essentially the same.

`\begin{gathered} \tan \theta=(4.5)/(7)\ldots(i) \\ \tan \theta=(AB)/(35)=(4.5)/(7) \\ AB=(4.5*35)/(7)=22.5m \end{gathered}`

Hence the height of tree is 22.5m.