# Ptolemy's Ptools

## Measuring the Altitude of a Model Rocket's Flight

### Materials needed:

2) Tape measure (at least 10 meters long)

3) Model Rocket (ready to be fired)

What to do:

Set up your model rocket in an open area, observing all SAFETY PROCEDURES.

Position one team member a measured distance, about 10 meters or more if possible, from the launch site. This person will measure the tangent angle of the rocket's flight with the quadrant. When the rocket takes off there isn't much time to take your measurement, so make sure to have this person practice a few times before countdown. If you have plenty of team members, you might want to have one person sight the rocket with the quadrant and another stand by to read the scale.

Look up the ratio that corresponds to the angle measured in the
tangent chart.

Multiply the ratio value by the distance from the launch site. The result will be how high the rocket went.

How it Works:

Similar triangles are triangles that have the same shape.

All three of their angles have the same measure.

The lengths of their corresponding sides are in the same proportion.

Right triangles have one angle that measures 90°. We can often assume a right triangle when conducting projects such as these. We can assume that the ground is approximately flat and that the rocket goes approximately straight up. This gives us a right triangle.

Since the sum of the three angles of a triangle ALWAYS equals 180°, by measuring a second angle in our triangle we can determine its shape.

By measuring the length of one side of the triangle (the distance from the launch site to the quadrant holder) we can determine the length of either of the other two sides of the triangle.

To transfer the data (measure of second angle and length of one side) into the desired results, a ratio (determined by the proportions of our triangle) is used as a multiplier on the side length measured. Since we want to know what the length of the opposite side from our measured angle is (how high the rocket went) we look up the multiplier for the tangent ratio.

We are using the properties of triangles to compare similar triangles.

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