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Real-Life Activities

Real-Life Math

You are a botanist working for a forestry service. One day your supervisor asks you to calculate the height of a very old tree.

Botanists measure tree growth over time because the rate of growth tells them a lot about the ecosystem. For example, the growth rate can show them the availability of water or nutrients in the soil. If you measure regularly, you can tell whether the amount of available water and nutrients has changed from season to season.

It is not easy to learn the height of a very tall tree. There are two ways to do it. One way involves extending a heavy piece of equipment up in the air until it reaches the tree top. However, this takes two botanists.

The other method uses trigonometry and an instrument called a clinometer. A clinometer is a small instrument that measures an angle. If you know the distance you are standing from a tree, and the degree of the angle that extends from your feet to the tree top, you can use trigonometry to figure out the tree's height. Trigonometry is a branch of mathematics dealing with measurements of the angles and sides of triangles.

We know from geometry that the angles in all triangles total 180 degrees. Imagine yourself standing several feet back from a tree. Your feet, the base of the tree trunk and the top of the tree form the three points of a right angled triangle.

You locate the tree, and use a measuring stick to find out that you are standing 71 feet away from the tree. Next, you take your clinometer and discover that the angle between you and the tree top is 31.8 degrees.