Question

Ravi is 1.82 m tall. He wants to find the height of a tree in his backyard. From the tree’s base he walked 12.20 m. along the tree’s shadow to a position where the end of his shadow exactly overlaps the end of the tree’s shadow. He is now 6.10 m from the end of the shadow. How tall is the tree?

Answer 1

Given: 

Height of Ravi ‘BC’ = 1.82 m. 

Distance of Ravi from the foot of the tree BD = 12.2 m. 

Length of the shadow of Ravi = AB = 6.10 m 

Let DE represent the tree. 

From the figure, △ABC ~ △ADE. 

Thus,\(\frac{AB}{AD}=\frac{BC}{DE}=\frac{AC}{AE}\)

Ratio of corresponding sides of two similar triangles are equal] 

\(\frac{6.10}{6.10+12.20} = \frac{1.82}{DE}\) 

DE = \(\frac{1.82\times18.30}{6.10}\) = 5.46 m 

Thus, the height of the tree = 5.46 m.