Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 17: Geometry at Work 239

The river measures 60 meters from W to A.

If you want to know if that big tree in your local park is as tall as the holiday tree in Rockefeller
Center, you’re not going to climb the tree with a yardstick. But you can go down to the park with
a friend on a sunny day and use the sun, your friend, and similar triangles to help you measure
the tree.

The sun will cause the tree to throw a shadow on the ground, and although you can’t easily
measure the tree, you can measure its shadow. Have your friend stand up nice and tall beside the
tree and measure his height and the length of his shadow. The tree and its shadow form the legs
of a right triangle (with a ray of sunlight as its hypotenuse). Your friend and his shadow make the
legs of a similar right triangle. You can set up a proportion to find the height of the tree.

If your friend is 5 feet tall and casts a shadow 2 feet long, and the tree’s shadow is 30 feet long,
your proportion will look like this.

Your tree is 75 feet tall, just a foot shorter than the 2013 Rockefeller Center tree.

WA

RE

WT

TR

x

x

x

12

100

20

20 1200

1200

20

 60









tree

tree’s shadow

5 friend

friend’s shadow

x

x

x

30

5

2

2 150

75

5

5

5