Which instrument is commonly used to measure tree height?

The clinometer is the correct instrument for measuring tree height because it allows users to determine the height by measuring the angle of elevation to the top of the tree from a certain distance away. By knowing the distance from the base of the tree and the angle of elevation, one can apply trigonometric calculations to derive the height of the tree.

In contrast, a compass is primarily used for navigation and determining directions, making it unsuitable for measuring tree height. Diameter tape is designed for measuring the circumference or diameter of a tree, not its height. An increment borer is a tool used in forestry to extract a core sample from a tree, which can provide insights into growth rates and age but does not measure height. Each of these tools serves specific purposes in forestry and tree management, but only the clinometer aligns with the requirement of measuring height effectively.