How to measure the height of a building

Look through your legs!

Some of the early ways of measuring the height of tall structures are still in use today. They require very few materials. Why not try some of these methods for yourself? If you try more than one way you can then compare your results to discover if the answers you get are close - they should be. After all, the building doesn't change its height because you change your measurement method! You might be surprised just how accurate you can be.

Native Americans had a very interesting and unusual way of seeing how high a tree was. They would bend over and look through their legs! They would walk far enough from the tree to a find a place where they were just able to see the top of the tree (from their upside down position). The distance from this place to the base of the tree was approximately the height of the tree.

Does it work? Actually it does and the reason is rather simple. For a normal, fit and healthy adult (one who can bend over in such a way), the angle that is formed as they look through their legs is approximately 45 degrees. Using what you know about the angles and sides of a triangle, this means that the angle between the tree trunk and the ground is fairly close to 90 degrees. The height of the tree and the distance from the tree to the person is about equal. 

Between finger and thumb!

Loggers are people who cut down trees. They learned a great deal from people who lived in forests for generations, like the Native Americans. They might be cutting down trees that are over a certain height and it is important that they have an easy way to estimate which of the trees around them are to be cut. You can try and estimate the height of a building using their method.

You will need a partner. One person stands at a distance from the building and extends their arms forward as fully as they can. They then bracket the building between the thumb and forefinger (the way you see artists in cartoons looking at an object they are going to draw). If the building is too big to fit in your finger frame, then walk farther back. Here's the tricky part! Without changing the distance between your fingers and keeping your thumb where it matches with the base of the building, flip your forefinger towards you. The distance between your thumb and forefinger should now run along the ground from the base of the building outward toward you. Your partner then needs to find the spot on the ground where your forefinger appears to be touching the ground (it is important that you keep your arm fully extended while you are doing this). Measure the distance of the ground from the building base to where you friend marked the spot - the distance on the ground equals the height of the building. This is quite easy, once you have the knack. Describing the method makes it sound way more complicated than it is.

Fancy trying a third method? Don't forget to be comparing the sizes that you are getting for the building height to see how they match up.

Measuring shadows

You will need a partner again, and another thing that you will need is a sunny day. You might have to pick your time for this experiment. Wait until the building casts a shadow then measure the length of the shadow. Stand next to the building and have a friend or parent measure your shadow. Be sure to do it as soon as you can after you measure the building shadow! Measure your height to find out how tall you are. Now for the good part - get those calculators out! You will need the 3 measurements: 

• the length of the building’s shadow
• the length of your shadow
• your height  

Divide the length of the building’s shadow by the length of your shadow. Then multiply the answer by your height. This will tell you how tall the building is!

(Building’s Shadow / Your Shadow) x Your Height = Building’s Height

Can you see why this works? Why not have a go?

Information from www.maths.org

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