Grade 10 · Right-triangle trigonometry
Art installation: Relate an acute angle to side ratios
Art installation investigation: relate an acute angle to side ratios. Change the quantities, follow the motion, and explain the result using the displayed mathematical relationship.
Predict what will happen, press Play, then pause and explain what changed. Every control also works without playback.
Watch the relationship
PausedHD animation studio
From experiment to screen.
Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.
Understand what you are seeing
The idea behind the motion.
For a fixed acute angle, the ratios of corresponding sides are unchanged by scaling a right triangle. Sine compares the opposite leg with the hypotenuse, while cosine compares the adjacent leg with the hypotenuse. The names depend on which acute angle is chosen. This investigation begins with hypotenuse h = 8; final acute angle = 40. Treat the named setting as a constructed classroom model, then explain which relationships would still hold if its numbers changed.
A relationship to keep
opposite = H sin θ; adjacent = H cos θ
Read the symbols alongside the explanation. A diagram shows the relationship; the assumptions tell you when it applies.
- STEP 1
Represent the given quantities
Identify the hypotenuse as the side opposite the right angle; read the chosen angle at the left vertex.
- STEP 2
Follow the changing model
Playback opens the angle from five degrees to the selected final angle while preserving hypotenuse length.
- STEP 3
Check and explain the relationship
Compare the side ratios with sine and cosine, then verify that the two squared legs sum to H².
Your turn to explain
Make a prediction. Test your reasoning.
Art installation: A right triangle has hypotenuse 8 and selected angle 40°. Find the opposite and adjacent legs.
Use the values specified in the question. Reset restores the initial values for this investigation.
Compare your explanation
Opposite ≈ 5.142; adjacent ≈ 6.128. Use sine and cosine of the same selected angle.
Work through a full lesson
Connect the animation to a worked example and practice questions.