Learn with Amar
Teaching video
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Grade 8 chapters and video availability01 · Read and understand
What you will learn
- Explain how to recover a right triangle's missing leg.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Squares, square roots, and the Pythagorean theorem.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
A right-triangle model has hypotenuse 13 m and one leg 5 m. Find the other leg.
Why this math matters
When the hypotenuse is known, the Pythagorean theorem finds a missing leg by subtraction of squares. Label the side opposite the right angle before substituting any lengths into the theorem.
Set up the model
A useful answer starts with clear assumptions:
- The triangle has a right angle.
- The 13 m side is opposite the right angle.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Recover a right triangle's missing leg
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A right-triangle model has hypotenuse 13 m and one leg 5 m. Find the other leg.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the quantities
5² + b² = 13²
Place the hypotenuse alone on the right side of the Pythagorean equation.
Apply the relationship
b² = 169 − 25 = 144
Subtract the known leg's square from the hypotenuse's square.
Check and interpret
b = 12 m; 25 + 144 = 169
Choose the positive square root because a length is positive.
The result
b = 12 m; 25 + 144 = 169
Choose the positive square root because a length is positive.
Common mistakes to catch
- Add the leg squares only when finding a hypotenuse; finding a missing leg requires subtraction.
- The hypotenuse cannot be identified by how a triangle happens to be drawn.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
A right triangle has hypotenuse 10 cm and one leg 6 cm. Find the other leg.
Show a hint
Subtract 6² from 10².
Reveal answer and explanation
8 cm
√(100 − 36) = √64 = 8.
Practice 2
Can a right triangle have hypotenuse 7 cm and a leg of 9 cm?
Show a hint
The hypotenuse must be the longest side.
Reveal answer and explanation
No
The proposed missing-leg square would be 49 − 81 = −32, impossible for a real length.
Take the idea with you
Label the side opposite the right angle before substituting any lengths into the theorem.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Test whether three sides form a right triangle
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