Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 17: Geometry at Work 243

Remember that tree you measured by using similar triangles? You needed the help of a friend to
make the second triangle, but what if your friend wasn’t available? What would you have done?

With the help of trigonometry, you could find the height of the tree without your friend. Stand
at the tip of the tree’s shadow and measure the angle to the top of the tree. The height of the
tree is the side opposite that angle, and the length of the shadow is the side adjacent to the
shadow. The opposite side over the adjacent side forms the ratio called the tangent.

In this case, you’d probably find the angle to be about 68r, and you know the length of the tree’s
shadow is 30 feet. You can find tan(68r) on a table or calculator and set up the problem like this.

Once again, the tree is 75 feet high.

tan A

opposite

adjacent

tan 68.2

30

30tan 68.2

30 2.5

x

x

x

75 x