How do I find the Height of the tree?

Question

A tree casts a shadow 10 m Long. at the same time, a sign post next to the tree  cast a shadow 4 m Long. the sign post is 2 m tall. how tall is the tree?

Answer 1

 

Set up as a proportion

 

   tree height         sign post height

  ------------------ = ------------------------

   tree shadow        sign post shadow

   height

 

   Let h = tree height

 

   h / 10 = 2 / 4

 

cross multiply

 

   4h =  2(10)

   4h = 20

     h = 5

 

Tree is 5 meters tall

 

Answer 2

The ratio of the height of Sign post to its length, is proportional to the ratio of the height of tree to its shadow length.

 

(Height of Sign post)/(Length of Sign post Shadow)= (Height of Tree)/(Length of Tree Shadow)

Let h = height of tree

Substituting the information given, we have: 2/4=h/10

Cross multiply: 4h=2×10

 

                      4h = 20

h=20/4

h=5

The tree is 5 meters tall.