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Pythagorean Theorem Solver
The Pythagorean theorem, step by step.
Type or photograph the two known sides of a right triangle. AskSia applies a^2 + b^2 = c^2 (or its rearrangement) to find the third side with every arithmetic step shown. 3D and distance applications supported.
Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
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asksia.ai/solver
98% · Verified
Problem
Find the area enclosed between y = x² and y = 2x in the first quadrant.
1
Find the points of intersection
Set the curves equal: x² = 2x → x(x - 2) = 0, so x = 0 and x = 2.
2
Identify which curve is on top
On (0, 2), 2x > x², so y = 2x is the upper curve.
3
Set up the area integral
A = ∫₀² (2x - x²) dx
4
Integrate term-by-term
A = [ x² - x³/3 ]₀²
Final Answer
A = 4/3 sq. units
Quick Answer
What is the Pythagorean theorem?
The Pythagorean theorem says that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a^2 + b^2 = c^2, where c is the hypotenuse (opposite the 90-degree angle). To find a missing side, rearrange: c = sqrt(a^2 + b^2) for the hypotenuse, or b = sqrt(c^2 - a^2) for a leg. The theorem only works for right triangles; for general triangles, use the law of cosines.
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why students use AskSia for Pythagorean Theorem.
Every step transparent, every answer self-checked.
Exact and decimal forms.
AskSia gives the answer in exact radical form (e.g., 5*sqrt(2)) plus a decimal.
Both
Pythagorean triples.
(3,4,5), (5,12,13), (8,15,17), (7,24,25), and more recognized.
Patterns
3D and distance.
Extends to sqrt(a^2 + b^2 + c^2) for 3D, and underlies the distance formula.
Extensions
Photo, paste, or type.
Snap handwritten or printed problems with your phone, paste from any online homework portal, or type with full LaTeX support.
Multi-modal input
Verified by AskSia.
Every answer gets a self-check pass. Sia catches sign errors and algebra mistakes before you submit your homework.
Self-checked
How It Works
Solve any Pythagorean Theorem problem in three steps.
Step 01
Enter the problem.
Type the expression, paste from your homework, snap a photo, or speak it. AskSia parses your input and identifies the structure.
Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02
AskSia picks the method.
Based on the problem structure, AskSia chooses the cleanest solution path and labels each step with the operation performed.
1
Set curves equal
x² = 2x → x = 0, x = 2
2
Set up the integral
A = ∫₀² (2x - x²) dx
3
Evaluate
A = [x² - x³/3]₀² = 4/3
Step 03
Read the verified answer.
Final result appears with a substitution or composition check. Practice problems on the same concept are one tap away.
Auto-generated diagram
Region between y = 2x and y = x² — area = 4/3
Available On
Solve anywhere
you study.
Every solve syncs across Web, iOS, and Android — start it at your desk, finish on your phone.
Web App
Full study studio
Split-panel interface with the worked solution on the left, the auto-generated diagram and AI tutor chat on the right.
Drag & drop image upload + LaTeX equation editor
Auto-generated diagrams render alongside steps
Side-panel AI tutor chat for hints and alt methods
Export to PDF, DOCX, Notion, or Google Docs
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Calculus
98% verified
1.4s
Step 4 of 4 · Evaluate
A = [x² - x³/3]₀² = 4/3
Mobile App
Snap & solve, anywhere
Open the camera, frame the problem, and the worked solution plus diagram appear in seconds.
One-tap snap-and-solve on iOS and Android
Pinch-to-zoom diagrams, swipe between steps
Auto-sync solves with your Web library
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98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
What the Pythagorean Theorem solver covers.
Find hypotenuse.
Given legs a and b, hypotenuse is sqrt(a^2 + b^2).
Hypotenuse
Find a leg.
Given hypotenuse c and one leg a, other leg is sqrt(c^2 - a^2).
Leg
Diagonal of rectangle.
Rectangle with sides a, b has diagonal sqrt(a^2 + b^2).
Geometry
Distance formula.
Distance between two points uses Pythagoras on coordinate differences.
Coordinate
3D distance.
sqrt(a^2 + b^2 + c^2) generalizes to three dimensions.
3D
Verify your homework.
Paste your candidate answer and the original problem. AskSia walks the work, flags any divergent step, and tells you the correct final value.
Answer check
Compare
AskSia vs. ChatGPT,
Photomath & Symbolab.
General chatbots hallucinate. Photo solvers stop at math. AskSia is built for actual coursework with verified accuracy, visual learning, and every subject.
| Feature | AskSia Solver | ChatGPT | Photo Solvers |
|---|---|---|---|
| Solution accuracy | ✓ 98% | ~70-85%, hallucinations | ~90%, math only |
| Auto-generated diagrams | ✓ Every solve | Inconsistent / broken | Graphs only, math-only |
| Step-by-step explanations | ✓ Numbered + plain English | Inconsistent depth | ✓ Math steps |
| Subject coverage | ✓ Math, Physics, Chem, Bio, CS, Econ | ✓ Wide but unverified | Math only |
| Photo input | ✓ Handwriting + diagrams + code | Photos OK, weak on handwriting | ✓ Math photos only |
| Answer verification | ✓ Self-checked before display | No verification | Math engine only |
| Tutor follow-ups | ✓ Hints, alt methods, ELI5 | ✓ General chat | Not available |
| Practice and flashcards | ✓ One-tap from any solve | Manual prompting | Not available |
| Code debugging | ✓ Python, Java, C++, SQL... | ✓ Yes | Not available |
| Free to start | ✓ Daily solves, no card | Limited model access | Steps locked behind paywall |
FAQ
Frequently asked questions.
Why does the Pythagorean theorem only work for right triangles?
Because the proof relies on the right angle creating perpendicular legs. The most common proof rearranges four copies of the triangle inside a square, and the rearrangement only works when the angle is 90 degrees. For non-right triangles, the law of cosines provides the generalization, with a -2ab*cos(C) correction term that vanishes when C = 90 degrees.
What is a Pythagorean triple?
A Pythagorean triple is a set of three positive integers (a, b, c) that satisfy a^2 + b^2 = c^2 exactly. The smallest is (3, 4, 5). Other primitive triples include (5, 12, 13), (8, 15, 17), (7, 24, 25), (20, 21, 29). They are useful because they give clean right triangles with integer sides, and they are generated by Euclid's formula.
Can the Pythagorean theorem give a negative answer?
No. Lengths are non-negative, and the theorem returns a sum (or difference) of squares followed by a square root, which is also non-negative. If you compute c^2 - a^2 < 0, that means a > c, which is impossible because the hypotenuse must be the longest side. AskSia checks for this case and flags an input error.
How does the Pythagorean theorem generalize to 3D?
By applying it twice. The distance from the origin to a point (a, b, c) in 3D equals sqrt(a^2 + b^2 + c^2). To see this, first find the planar distance sqrt(a^2 + b^2) from origin to (a, b, 0), then apply Pythagoras again with this planar distance as one leg and c as the other to get the 3D distance. The pattern extends to higher dimensions naturally.
How accurate is AskSia?
AskSia hits 98% accuracy on standard high school and college coursework, measurably higher than ChatGPT, Photomath, and Symbolab on the same problem sets. Accuracy comes from subject-specialized models, a symbolic verification pass that catches arithmetic errors, and a self-check step that re-derives the answer before showing it to you.
Can I get practice problems and flashcards?
Yes. After any solve, ask Sia to generate similar practice problems at SAT, ACT, AP, IB, or college difficulty, or build a flashcard set on the underlying concept in one tap. Useful for exam prep and spaced repetition before a quiz, midterm, or final.
How much does AskSia cost?
AskSia has a free plan that includes daily solves across all subjects. AskSia Pro and Super include unlimited solves, advanced subjects, the full AI tutor companion, exports, and priority response speed. See pricing for details.
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