Introduction: Measuring Height Using Trigonometry (Measuring Tape Hack)

Measuring height using a measuring tape could be quite stressful. When you try to measure something that is too high, the measuring tape will start to bend backwards. Recently I saw some workers having difficulty measuring the height of the walls in my house when they want to install a canopy on the terrace of the house. Two people with the help of a ladder are required to measure the height of the wall, one person will hold the end of the measuring tape and the other one will look at the measurement.

This incident inspired me to hack a measuring tape, so it can measure height horizontally. Using this hack, we no longer need to worry about measuring height that is hard to reach using a typical measuring tape.

Difficulty level: Easy

Time needed: About an hour

Step 1: How It Works

Special Triangles in Trigonometry

In this project, I use the special triangles with 30º - 60º - 90º or 45º - 45º - 90º. I apply these formulas to my measuring tape, so it can measure height by knowing the length of one side and two angles from the triangle.


Thales' Shadow

This project is also inspired by a Mathematician named Thales who measures the height of a pyramid just by using the shadow of a short pole.

Step 2: Things You'll Need

You can get most of the things needed in this project from your local hardware store and/or bookstore.

Measuring Tape (x1)

Laser pointer (x1)

Laser cut 2mm acrylic (x1)

Scissor/cutting pliers (x1)

White color aerosol spray paint (x1)

Fine tip black marker (x1)

Phillip screwdriver (x1)

4 inch cable tie (x2)

Feel free to download and edit my design

Step 3: Painting and Remarking

Painting

Prepare your measuring tape and pull your measuring tape until it reaches the longest possible value. (you will need large place to do this step). Cover the measuring tape in thin layer using white aerosol spray paint. You can put your measuring tape above used newspapers to prevent stain on the floor. Please make sure the paint is dried before you roll the measuring tape back, otherwise the paint will make the inside of the roll sticky.

Remarking

Use a ruler to measure the location where you need to mark. Every 1cm in the Measuring tape is about 0.577cm (1÷√3), so I use multiple of 5 cm which means I will mark the measuring tape in every 2.886 cm (5÷√3).

Step 4: Screwing the Laser Cut Acrylic

Unscrew the belt clip and the screw the laser cut acrylic to the measuring tape.

Step 5: Attach the Laser Pointer

Insert your cable ties into your laser cut acrylic (as shown in the picture). Use the cable ties as a strap to hold the laser pointer and the tighten it. Cut the remaining flap using scissor or cutting plier.

Step 6: Done :)

Here is a demonstration video, you can skip the video to 2.20 to watch the demonstration part.

Hope you like this project, and please vote this project for "Hack Your Day Contest". Every vote is highly appreciated.

P.S. The guy in the video is my little brother

Comments

author
alfadog67 (author)2016-02-17

If you put the laser at a 45-degree angle instead of 60, you won't need to redo your tape measure.

author

Yes exactly, but by using 60º you won't need much floor space compared to 45º.
Using larger number of angle will reduce the length of floor space needed, but the results may be less accurate.
Thanks for the input ;)

author

Yes, excellent observation! Pop quiz: at what angle would your laser need to be to make the tape exactly half of the height? (Or the height exactly double the tape)?

author

To make the tape half of the height I will need about 63.4º

Method: tan-1(2) = 63.43498...

author

Thank you. That's just over 5% more than 60, and as you mentioned, a bit less accurate. Using your pictured calibration technique, I'd not even need to know the angle, but only the base and leg of the right triangle. Eureka! Then I could simply double the measured base to get the height. Please excuse my thinking out loud; it's just that I love trig, but I'm out of practice, and I find your project thought-provoking and interesting. Also, I can't paint well at all ;-)

author

Yeah I know, right? Trig can be really interesting!

Thanks for the idea ;-)

author
moncton (author)2016-02-14

Love it!!!!

author
Samuel_Alexander (author)moncton2016-02-14

Really glad you love it.

author
StephanP1 (author)2016-02-14

Very clever, you has my vote. How accurate is it?

author

Thank you!

For measuring the height of one to two story building it is still relatively precise. Maybe there is about 1-2% error tolerance.

author
ThomasK19 (author)2016-02-13

I know that woodworker use such an instrument (not with a laser pointer but a spyglass) to measure the height of trees. But this is a great idea. Of course it's necessary to have a perpendicular angle in the base to get exact results. But else this is really smart.

Your little brother is also a smart one :-)

author

Thanks!
Yes, every angle needs to be really accurate in order to show accurate results.

author
NTT (author)2016-02-13

This is great! And superbly presented. Well done, and thank you for sharing. Keep them coming!

author
Samuel_Alexander (author)NTT2016-02-13

Thanks!
There will be more projects coming soon ;)

About This Instructable

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Bio: I am Samuel Alexander, a 11th grade student at Cita-Hati High School in Surabaya, Indonesia. Since I was kid I have been interested in making ... More »
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