We home educate our children and one approach we take is to think up and solve problems. When solving one of these, **“how can you measure how tall a tree is?”**, the Tan-o-meter was born!

The maths is straightforward. You measure yourdistance from the treeand the angle to the top of the tree. Multiply the distance by the Tan of the angle and you get the height. Its super-simple to make using a paper-plate, straw and piece of string. You will need a protractor to mark the gage.

Iused the Tan-o-meter inthe MSA section of a Lean Sigma course I recently ran to gather data for a gage R&R, here is how. Split into teams and ask themto create the device. From one end of a desk, have each team membertake turns to measure the width of 5 random objects at the other end of thedesk. This is done by aligning the device at right angles (by eye) to one end of the object and measuring the angle to the other.Then measuring the distance to the object.

The data can be used for the Gage R&R plus an opportunity to run a fish-bone on where the measurment error occurs with associated FMEA plus data can be used in analyse.

If anyone finds this of use then keen to get feedback, any questions please let me know.

The next problem we are looking to solve is, **how can you measure the diameter of Jupiter?** This has taken us to Kepler’s 3rd law and the fixed speed of planet rotation around the Sun. Am now negotiating with a local observatory to see if we can measure the time Jupiter obscures a distant star. Then we will have cracked it….

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There’s a much easier way, that doesn’t require Tan tables. I did this with a walking party who wanted to know the height of a monument. Somebody puts their head to the ground at a paced-out distance from the object and observes when my head is at the same relative height to the top of the object as I approach. As I am 6 feet tall, and the distance from me to the observer measurable, the triangulation maths are straightforward.

I also know accurately my pace length.

We did this quicker than those who counted the layers of stonework, and both answers were within a reasonable error margin of each other.

Thanks for the comment Colin.

Just to say I do have any ulterior motive in using Tan in that its for home education of the kids and gives them a practical understanding.

As kids, we compared the length of the shadow of the object to the length of our own shadow and multiplied their ratio with our height to find out the height of the object.

Thanks Erny, this sounds like fun, I will try this and Colin’s one out.

Keep them coming!

As an amateur astronomer I have measured the diameter of Jupiter, as well as the Moon, Mercury, Venus, Mars and Saturn. Timing the transit of a distant star is not too useful as ithat does not occur too often. Contact me at ealanni at windstream dot net to discuss/learn more.

Nice one Eugene! Will be in contact next week, thanks Robin