Using Similar Triangles to measure things we can’t reach.
You know that similar triangles are triangles that are the same shape but a different size. This means that the lengths of the sides are in the same ratios.
4 5
3
6
Let’s say you were told that these two triangles were similar. You can see that the bottom side of the larger triangle is twice the size of the corresponding side in the small triangle. You now know that the vertical side of the large triangle will be 8 and the other side will be 10.
The river.
Here you need to measure the width of the pirana infested river (pirana shown!) You notice a stationary dinosaur directly opposite the cactus. Walk 10 m along the river and leave an avocado at that spot. Now walk a further 5 m and leave your cat there. Now walk directly inland until the avocado and the dinosaur are lined up. The distance from the cat to where you are standing will be half the width of the river. Can you see why?
Go and measure the width of the river outside. Where are you likely to be inaccurate? Check your answer with a tape measure and comment on the discrepancy.
The Tower.
Choose a high point that you will be able to check with a tape measure later. Go to the base of your tower and step out across flat ground 9 paces and mark that spot. Take one further pace. Get a partner to stand a metre rule vertically on the marked spot (zero on the ground). Put your eye on the ground at the spot that is 10 paces from the tower. Sight up through the ruler to the top of the tower. Can you see the two similar triangles you have created? How much bigger is the big triangle? Note the point on the ruler that the top of the tower is in line with. What is the height of the tower?
9 paces
1 pace
Where are you most likely to make errors here? How could you improve it?
Did the paces have to 9 and 1?
Why did I suggest 9 and 1?
Did they have to be paces?
Invent your own system of lengths and distances and repeat the measurement?
Was your choice of lengths and ratios better? Why?