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.