NUMBAT OER - Open Educational Resources

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


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

H=h+d.tan α

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.