Step by step
The question
Question: find the shadow x of the stick.
A 6 m tree has a 4 m shadow.
At the same time, the stick is 1.5 m tall.
1 Two similar triangles
The sun's rays come in at the same angle.
So the two dashed lines are parallel.
The tree and the stick both stand straight up: a right angle at the bottom.
Same angles, so the two triangles are similar.
One is a bigger copy of the other.
2 Match the sides
Matching sides go together.
The height goes with the height.
The shadow goes with the shadow.
3 Find the scale factor
The scale factor k says how many times bigger.
We know both heights: 6 m and 1.5 m.
k is big over small.
Careful!
Never put a height with a shadow.
Height with height, shadow with shadow.
6 divided by 1.5 is 4.
The tree's triangle is 4 times bigger.
4 Find x
x is in the small triangle.
Its partner is 4 m.
The small one is 4 times smaller, so we divide by 4.
That is 1.
So the shadow of the stick is 1 m.
5 Check
Let's check: x with its partner.
4/1 is 4, the scale factor.
The tree is taller than its shadow.
So the stick is taller than its shadow too.
It makes sense!
Let's look back.
First: two similar triangles.
Then: match the sides.
Then: find the scale factor.
Then: find x.
Last: check.