Model Rocketry Mathematics
See http://www.clarku.edu/~djoyce/trig for a great introduction to Trigonometry that is beyond the
scope of this assignment, but is really interesting information if you enjoy math.
Typically, students wait until after taking Algebra and Geometry before they learn how to perform
trigonometric functions. However, since you are a gifted group of young scholars, you are ready to learn
to use a trig function for this laboratory. This should provide you experience in using this math, and
later, when you need to learn the theory of it, may help you to see that you have already used it.
The important basics of this trigonometric function (for the use in this class) are that we are working
with right triangles. Right triangles have a ninety degree angle in them. Mathematicians have a standard
way of labeling a right triangle as shown in the diagram below that I took from Wikipedia.
If you want a whole bunch more information about triangles you can consult Wikipedia at the following
link. http://en.wikipedia.org/wiki/Triangle (Be sure to double check the information with another
source, because anyone can edit Wikipedia).
For your rocket launch, we will know the length of one side of our triangle and two angles of that
triangle. According to the wonder of mathematics and similar triangles we can use a trig function to find
out the length of the other sides and angle of the triangle. In our case we only care about the height our
rockets flew as shown in the diagram you will need to draw beside the triangle above. I will draw it on
the board for each class. We will measure angle A from 25 meters away, so we will know the length of
the adjacent side.
We will use the tangent function on a calculator to calculate the heights of the rockets. For use in this
class, the tangent function is a ratio between two sides of a right triangle. Tangent could be found by
dividing the side of the triangle opposite the angle we measure for each rocket by the side adjacent to
the angle we measure for each class. Unfortunately we don’t know the length of the side opposite the
angle. To get a better idea of what this means we will use a calculator to find what the tangent is for the
angles below after sketching each triangle on the board:
Triangle
drawing
Measurement Tangent of
of angle A
angle A
5
25
45
75
85
We will use colored pencils to sketch the shape of each triangle from the board into the space below to
show how this number is calculated by your calculator. The color of the adjacent side of my triangles is
___________. The color of the opposite side of my triangles is ___________. The hypotenuse of my
triangles is colored __________.
Even though we could calculate the height from the original formula that is shown below, I like to do
some algebra and move the numbers around to make them more useful to us.
Tan A = opposite
adjacent
I want to solve for the side opposite angle A. I can multiply both sides of an equation by the same
number and not change the value of the equation as follows.
(adjacent) X Tan A =
opposite X (adjacent)
adjacent
Notice how the adjacent sides on the right can be cancelled out. This leaves a formula that is easier for
us to use for everyone’s rocket in the class.
(adjacent) X Tan A = opposite
I can substitute 25 meters in for the length of the adjacent side, because that will be the same for each
rocket. Now the formula becomes
(25 meters) X Tan A = opposite
Once we launch the rockets we will find the measure angle A for each rocket when at the highest point
of its flight. Then we can find the tangent of these angles, multiply that number by 25 and we will be
able to calculate approximately how high each one goes. Here are a few chances to practice before we
get the actual values.
Rocket launched by
Angle at highest point
Julie
Todd
Sarah
Mr. Fin
35
55
80
43
tan A
Height = 25 meters X
tan A
Save this paper so you will have it for reference when calculating the heights for the class. I will give you
a spreadsheet of the angles.