Canada Builds

Measuring Height

The law of Tangents can help you to measure the height of a building without having to go up on the roof. Refer to the diagram below. You want the value of 'a' or the vertical height of an object (possibly a tall building). Measure along the ground from the object to a telescope or survey transit to get a value for 'b'. Measure the angle created to sight the top of the building. In the example below a value of 31.66 degrees is indicated. these two values can now be used to calculate the height (a). This technique is also useful to measure the height of large trees.

The excel worksheet below can be used to test this geometric theory. In the case of the example shown above, the horizontal distance from the building to the scope is 30000 mm or 30 metres and the angle measured from the horizontal to the top of the building is 31.66 degrees. These two values are shown in red below and the height is then calculated using the law of tangents. If you click once on the sheet below, you can use the sheet as your own calculator.