First assignment

Using the properties of similar triangles, your group will measure the height of a tree in each of your school grounds and compare notes. You must use all three methods and afterwards discuss the accuracy of the 3 methods that are given with your foreign friends.

The final product for the group is a blog post here on the blog showing your calculations and your discussion.

Also each group must keep a log to show your process – what did you do? Which problems occurred? How did you overcome obstacles? And so on. This must also be shown in a blog post. You can use pictures in you post.

Method 1 – Stacking friends

Here you need a friend.
Your friend stands beside the thee.
Walk about 30 meters away from the tree.
Use your fingers to measure your friend.
How many times can your friend be put on top of himself to reach the top of the tree?
Measure your friend’s height and times it to get the height of the tree.

Method 2 – stick in hand

Find a stick that is at least the length of your arm. Hold the stick vertically in your stretched arm. The stick above your hand should have the same length as your arm. You can check it by resting the stick on your stretched arm. If the end reaches your shoulder it is right. 

Stand in front of the tree. Remember to hold the stick vertically out in front of you with your arm stretched.

Walk backwards until the tree is completely covered by the stick in the height – it should not be longer or shorter than the tree.  Look over the stick to see the treetop flush with the top of the tree and look down to see the bottom of the stick flush with the root of the tree. (See pic.)

The distance from the tree to where you are standing is now the same height as the tree. Measure the distance to get the height of the tree.

We are using to similar triangles to find the height of the tree.
On the drawing below you see the two similar triangles inside each other.  The big triangle has the sides A,B and C. The smaller triangle has the sides a, b and c. The angles in the small triangle are the same as in the bigger triangle. Therefore we know that they are similar.

The length of your arm is the same distance as the distance from your eye to where you are holding the stick. That means that the distance from your eye to the stick (a) is the same as the length of the stick (b) - a=b.
The same goes for the large triangle – A=B, because:
In two similar triangle the ratio between the sides are the same

A = B = C
a     b    c

So when a=b, then A=B. Meaning the distance from you (A) = the height of the tree (B)

Method 3 – The sun

This method is only workable when the sun is out and there has to be room around the tree so you can where the shadow is cast.

Find a stick and stick it vertically into the ground. Measure the length of the stick (p).
Measure the length of the shadow of the stick (s)
Measure the shadow of the tree (t)

The height of the tree is:

h = t x p / s

(see youtube video for explanation http://www.youtube.com/watch?v=LhEe0kB4QIs)