Figure 1. General Sherman, the world’s largest living tree. (credit: Mike Baird, Flickr)

The world’s largest tree by volume, named General Sherman, stands 274.9 feet tall and resides in Northern California.^[1] Just how do scientists know its true height? A common way to measure the height involves determining the angle of elevation, which is formed by the tree and the ground at a point some distance away from the base of the tree. This method is much more practical than climbing the tree and dropping a very long tape measure.

In this chapter, we will explore applications of trigonometry that will enable us to solve many different kinds of problems, including finding the height of a tree. We extend topics we introduced in Trigonometric Functions and investigate applications more deeply and meaningfully.