Height of a Tree

This morning in math class we worked on our own for a little while, finishing off some tests and surveys from last week. Later we worked together to figure out the height of a tree using some simple trigonometry concepts.

In the activity, we were asked to accurately find the height of a tree using only a measuring tape and a protractor. So we brainstormed how to figure out the different measurements we could take with our tools... We had to assume that we couldn't just climb up the tree and dangle the measuring tape down to the bottom!

First we drew a tree outline on the chalkboard to help us visualize the dimensions. Using the tape measure, we then measured the distance between the chalkboard and where we were standing. (This formed two sides of a right angle triangle.) Then we put the protractor at our feet and measured the angle from the top of the tree down to the pivot point of the protractor (with the help of a bit of string).

So what was the calculated height of the tree? It was 183 cm multiplied by the tangent of 49, or about 211 cm tall... and the measuring tape confirmed it!