Step by step
The question
Question: find the height x of the person.
A 10 m tree has a 4 m shadow.
At the same time, the person has a 0.6 m shadow.
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 person 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 shadows: 4 m and 0.6 m.
k is big over small.
Careful!
Never put a height with a shadow.
Shadow with shadow, height with height.
4 divided by 0.6 is 20/3.
The tree's triangle is 20/3 times bigger.
4 Find x
x is in the small triangle, so we go from big to small.
20/3 is 20/3.
Turned upside down, it is 3/20.
10 times 3 is 30.
Divided by 20, that is 1.5.
That is 1.5.
So the height of the person is 1.5 m.
5 Check
Let's check: x with its partner.
10/1.5 is 20/3, the scale factor.
The tree is taller than its shadow.
So the person is taller than their 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.