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.