Grade 8 · Right triangles
School garden: Recover a right-triangle distance
School garden investigation: recover a right-triangle distance. 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 right triangle, the square of the longest side equals the sum of the squares of the two legs. Square areas provide the comparison; the hypotenuse itself is the positive square root of their sum. Adding side lengths is not a substitute for this theorem. This investigation begins with first leg a = 2; second leg b = 3. Treat the named setting as a constructed classroom model, then explain which relationships would still hold if its numbers changed.
A relationship to keep
c² = a²+b²; c = √(a²+b²)
Read the symbols alongside the explanation. A diagram shows the relationship; the assumptions tell you when it applies.
- STEP 1
Represent the given quantities
Locate the marked right angle and identify the two legs meeting there.
- STEP 2
Follow the changing model
Playback reveals the two square-area contributions beside the triangle and their combined total.
- STEP 3
Check and explain the relationship
Take the positive square root to recover a length, then square the answer to check the original identity.
Your turn to explain
Make a prediction. Test your reasoning.
School garden: A right triangle has legs 2 and 3. Find the hypotenuse.
Use the values specified in the question. Reset restores the initial values for this investigation.
Compare your explanation
√(13) ≈ 3.606 length units. The positive root represents a length.
Work through a full lesson
Connect the animation to a worked example and practice questions.