Obtuse triangle checker
Sides 3, 4 and 6 form an obtuse triangle, because 3² + 4² = 25 is less than 6² = 36. Enter any three side lengths to get a yes or no with that comparison, no angles needed. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- A
- 3
- B
- 4
- C
- 6
- Longest side
- 6
- Shorter squares sum
- 25
- Longest square
- 36
- Comparison
- 25 < 36
An obtuse triangle is a plane triangle that contains exactly one interior angle greater than ninety degrees. When only the three side lengths are known, you do not need to compute those angles at all: the converse of the Pythagorean theorem classifies the triangle from the squares of the sides. Sort the sides so that c is the longest, then compare a squared plus b squared with c squared. If the sum of the two shorter squares is smaller than the longest square, the angle opposite the longest side is obtuse and the triangle itself is obtuse. If the two quantities are equal the triangle is right; if the shorter squares add to more than the longest square the triangle is acute.
How the converse of Pythagoras decides an obtuse triangle
The Pythagorean theorem says that a plane triangle is right-angled if and only if the square of one side equals the sum of the squares of the other two. The converse and its two companions for acute and obtuse triangles use the same three numbers. Label the sides a, b, and c with c the longest.
Then a squared plus b squared compared with c squared tells you the type of the angle opposite c, which is always the largest angle. When a squared plus b squared is less than c squared, that largest angle is greater than ninety degrees, so the triangle is obtuse. When the two quantities are equal the largest angle is a right angle.
When a squared plus b squared is greater than c squared every angle is acute. You never need inverse cosine for a yes-or-no obtuse test: the comparison of squares is exact for integer sides and stable for ordinary decimals once a tiny relative tolerance absorbs floating-point noise around a near-right triple. The test is meaningless until the three lengths form a triangle at all.
The strict triangle inequality requires that each pair of sides sums to more than the third side; otherwise the points are collinear or the lengths cannot close. Degenerate cases such as one, two, three have zero area and are rejected rather than labeled. Because a plane triangle can have at most one obtuse angle, it is enough to test the longest side: if that opposite angle is not obtuse, none of the others can be.
What you enter, what you get, and what is refused
Every side must be strictly positive: zero or negative lengths are not sides of a Euclidean triangle. A triple such as one, two, ten cannot close and is rejected with a message that the sides cannot form a valid triangle. Example: three, four, six yields obtuse true because nine plus sixteen is twenty-five, which is less than thirty-six.
Three, four, five is the classic right triple, so obtuse is false. Five, five, five is acute, so obtuse is false. Failed validation is not billed.
What you can do with it
Homework checks from three sides
Let students submit three side lengths and verify the converse-of-Pythagoras obtuse test without computing inverse cosine by hand.
LMS auto-grading of obtuse items
Mark “is this triangle obtuse?” items with a deterministic oracle that rejects illegal sides instead of returning a silent false.
FAQ
How do I tell if a triangle is obtuse from its three sides?
Send positive finite sides a, b, and c.
What happens if the sides cannot form a triangle?
Zero, negative, missing, or non-finite sides, and any triple that fails the strict triangle inequality, are rejected and not billed.
Is a right triangle reported as obtuse?
No. A right triple such as 3, 4, 5 has equal squares, so obtuse is false. Only a strictly larger longest square returns true.
Do I need to put the longest side in field c?
No. The checker sorts the three lengths internally. Any order of a, b, and c is accepted.
Can a triangle have more than one obtuse angle?
No. A plane triangle has at most one obtuse angle, and it always sits opposite the longest side. That is why the check only compares the longest side with the other two and never needs to look at every angle.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/math/obtuse-triangle \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"a":3,"b":4,"c":6}'const res = await fetch("https://api.kit.forhosting.com/math/obtuse-triangle", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"a": 3,
"b": 4,
"c": 6
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/obtuse-triangle",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"a": 3,
"b": 4,
"c": 6
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/obtuse-triangle", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"a":3,"b":4,"c":6}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"a":3,"b":4,"c":6}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/obtuse-triangle", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"a": 3,
"b": 4,
"c": 6
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.obtuse_triangle",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
This obtuse triangle checker accepts three positive side lengths, rejects any triple that cannot form a valid triangle, and returns a boolean.
Input contract, response shape, and error behaviour
POST a JSON body with three required finite numbers: a, b, and c, the side lengths in any consistent unit. Aliases side_a, side_b, side_c and side1, side2, side3 are accepted so scripts that already use textbook labels do not need a rename step. Each field may arrive as a JSON number or as a numeric string; missing fields, empty strings, and non-finite values fail with invalid_input naming the field. On success the body echoes a, b, and c, sets obtuse to true or false, reports longest_side, shorter_squares_sum, and longest_square, and includes a short comparison string plus a formula restating the converse of Pythagoras. The endpoint does not return the degree measure of the obtuse angle, does not classify by side equality as scalene or isosceles, and does not accept angles; those are different search intents served by other capabilities.
Where an obtuse-from-sides checker earns its keep
Classrooms and tutoring platforms use an obtuse triangle checker so learners can confirm the converse-of-Pythagoras test on arbitrary side triples without mixing that test up with the angle-sum classifier that needs degrees instead of lengths. Failed validation does not consume balance. Exam-prep generators and LMS auto-graders need a deterministic oracle that marks illegal sides as invalid_input instead of silently returning false, which a buggy grader might treat as a successful not-obtuse answer. CAD macros, mesh tools, and simple geometry notebooks often know three edge lengths from a sketch and only need a boolean before branching: an obtuse corner may require a different fillet, a different UV layout, or a warning that the triangle is badly shaped for a finite-element element. Keep requests small, pin the obtuse boolean in tests, and you get a reproducible side-length check for homework, LMS plugins, and edge workers without standing up a computer-algebra system of your own.
Integration use cases
Mesh and CAD branching
Branch on a boolean when three known edge lengths make an obtuse corner that needs a different fillet, UV layout, or element warning.
Technical questions
What does the obtuse triangle checker cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.