Question

a wall that is 4 ft. 3 in. tall is next to a tree. the figure shows the shadows that they cast. what is the height of the tree in feet and inches?

Answer 1

`Tree = 17ft`

Explanation:

Given

`Wall = 4ft\ 3in`

`Wall\ Shadow = 6ft`

`Tree\ Shadow = 24ft`

Required:

Determine the height of the tree

To do this, we make use of the following equivalent ratios

Wall : Wall Shadow = Tree : Tree shadow

Substitute values for Wall, Wall Shadow and Tree Shadow

`4ft\ 3in : 6ft = Tree : 24ft`

Convert all units to ft

`4ft+ 0.25ft : 6ft = Tree : 24ft`

`4.25ft : 6ft = Tree : 24ft`

Convert to fractions

`(4.25ft)/(6ft) = (Tree )/( 24ft)`

Cross Multiply

`Tree * 6ft = 4.25ft * 24ft`

`Tree * 6ft = 102ft^2`

Make Tree the subject

`Tree = (102ft^2)/(6ft)`

`Tree = (102ft)/(6)`

`Tree = 17ft`

Hence, the tree is 17ft tall