How to Figure the Height of a Large Flagpole
- 1). Measure the distance from the base of the flagpole to a nearby point. About 20 or 30 feet is about right. Make sure the point you choose is at the same elevation as the flagpole's base. Place the telescope at this point.
- 2). Focus the telescope with the top of the flagpole at the center of the image. Write down the angle of elevation indicated by the telescope.
- 3). Calculate the height of the large flagpole. The height is equal to the tangent of the angle of elevation multiplied by the distance between the flagpole base and the telescope plus the height of the telescope. For example, suppose the telescope is 4 feet high and the distance to the flagpole is 30 feet. If you've measured an angle of elevation of 50 degrees the tangent is 1.192 (from your calculator or trigonometric tables). Multiply 30 feet by 1.192 and add 4 feet. The height is 39.76 feet.
- 4). Estimate the height of a large flagpole using the shadow it casts. Locate a nearby object with a clear shadow short enough to measure with a measuring tape (a fence post is perfect). Measure the height of the object and the length of its shadow.
- 5). Measure the length of the flagpole's shadow immediately. Do not delay because movement of the sun will alter the shadow's length and make your calculation useless.
- 6). Compare the lengths of the two shadows. The ratio of the height of the flagpole to the length of its shadow is proportional to the ratio of the height to the shadow length of the other object you measured. The formula is H/s(1) = F/s(2) where H is the height of the smaller object, F is the height of the flagpole, and s is the length of the respective shadows. For example, if a fence post 4-feet high casts a 3-foot shadow, and the flagpole casts a 30-foot shadow, the flagpole is about 40 feet high.
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