## 2. How high is that tree?

A simple application of trigonometry is to calculate the height of an object that cannot be measured directly. For instance, it is seldom practical to measure the height of a tree with a tape measure, but it can be accomplished easily by using an instrument called a clinometer to measure the angle of a line between the horizontal and a line from the observer to the top of the tree, when the distance of the observer from the base of the tree is known:

tan α = (height of tree – height of observer)/distance to base of tree

then,

height of tree = (tan α/distance to base of tree) + height of observer

Obviously, if the clinometer were set on the ground, level with the base of the tree, there would be no need to include the height of the observer in the calculation.