Question

Marta wanted to find the height of a tree by placing a stake in the ground to make a shadow which could then be compared to the length of the tree's shadow

Answer 1

`DF = 56.4`

Explanation:

Given

See attachment for tree and the stake

Required

The height of the tree

From the attachment, the height is represented by DF.

DF is calculated using the following equivalent ratios

`AC:CB = DF:FE`

This gives:

`5.6:4.2 = DF:42.3`

Express as fraction

`(5.6)/(4.2) = (DF)/(42.3)`

Solve for DF

`DF = (5.6)/(4.2) *42.3`

`DF = (5.6*42.3)/(4.2)`

`DF = (236.88)/(4.2)`

`DF = 56.4`