Grade 8 · Recover a right-triangle distance · 300 of 750
Recover a right-triangle distance · practice 29
A right triangle has perpendicular legs 3 and 8. Find its hypotenuse. Follow the calculation, then test the quantities in the animated example.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
01 · Make a prediction
Your practice question
A right triangle has perpendicular legs 3 and 8. Find its hypotenuse.
Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.
A starting point
Add the leg squares, then take the nonnegative square root.
Work through the reasoning
Step 1
Translate the givens
The leg squares are 3² = 9 and 8² = 64.
Step 2
Calculate with the model
The hypotenuse square is 9 + 64 = 73.
Step 3
Check and interpret
Take the positive length: h = √73 ≈ 8.544. Squaring the exact root recovers the sum of leg squares.
The answer
Hypotenuse = √73 ≈ 8.544 length units.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.
Watch the relationship
PausedHD animation studio
From experiment to screen.
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The mathematical idea
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. Starting quantities: First leg a = 3; Second leg b = 8.
c² = a²+b²; c = √(a²+b²)
03 · Reflect and transfer
Explain what changes and why.
Why does the theorem require a right angle between the two given legs?
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.