Sin triangle calculator
With a 30° angle and an opposite side of 5, the hypotenuse is 10, because sine is opposite over hypotenuse. Enter one acute angle and either the opposite side or the hypotenuse to get the other, plus the complementary angle. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Angle
- 30
- Side
- 5
- Known side
- Opposite
- Value
- 10
- Complementary angle
- 60
- Right angle
- 90
- Opposite
- 5
In a right triangle the sine of an acute angle is the ratio of the opposite leg to the hypotenuse: sin(θ) equals opposite over hypotenuse. That single identity is enough to recover the missing side when one acute angle and one of those two sides are already known. This sin triangle calculator takes the known angle in degrees, a positive side length, and a role that says whether that length is the opposite or the hypotenuse. It then returns the missing length from the sine ratio, together with the complementary acute angle that completes the one-hundred-eighty-degree angle sum next to the right angle.
What sine means in a right triangle and how the missing side is locked
Sine in a right triangle is not a general-triangle law of sines and it is not a full SOHCAHTOA sweep. It is the one ratio opposite over hypotenuse, written sin(θ) = opposite / hypotenuse, where θ is an acute corner and the right angle sits opposite the longest side. If you already know θ and the opposite leg, divide that leg by sin(θ) to recover the hypotenuse.
If you already know θ and the hypotenuse, multiply the hypotenuse by sin(θ) to recover the opposite leg. Those two rearrangements are the entire solver. The adjacent leg is deliberately out of scope: cosine, not sine, pairs adjacent with the hypotenuse, and reaching the adjacent side through sine would mean swapping to the complementary angle first, which is a different classroom move and a different search.
The complementary acute angle is still returned, because a right triangle always closes with ninety degrees at the right corner and one hundred eighty degrees in total, so the other acute is exactly ninety minus θ. A classroom check is immediate. Thirty degrees with opposite five must produce sine one half and hypotenuse ten.
Thirty degrees with hypotenuse ten must produce opposite five. Forty-five degrees with opposite one must produce hypotenuse root two. Sixty degrees with hypotenuse two must produce opposite root three.
Special classroom angles use exact textbook sine so those goldens stay clean; every other acute angle uses the ordinary degree-to-radian conversion θ times pi over one hundred eighty and the host sine. Every step is elementary trigonometry on two scalars, so the result is deterministic, has no iteration, and never depends on the clock or a random seed.
Practical tips, limits, and when a sine-only solve is the right tool
Angles are degrees only in the public contract; convert from radians in your client if your sensor stack uses radians. When teaching, prefer paired examples: thirty degrees with opposite five for the classic double-the-leg hypotenuse; the same angle with hypotenuse ten to show the inverse multiply; and an angle of zero, ninety, or one hundred twenty to demonstrate the hard rejection path that protects callers from a degenerate or obtuse corner.
Prefer this contract when the given angle and the given side are already named opposite and hypotenuse in the figure — typical in SOH drills, angle-of-elevation opposite-over-hyp checks, and ramp-rise problems. If you already know two legs and want the hypotenuse, Pythagoras is a different search; if you know the adjacent side and the same acute angle, use a cosine solver instead of forcing adjacent into this sine contract.
What you can do with it
Ramps, roofs, and angle-of-elevation takeoff
Turn a measured slope angle plus a rise or a slope length into the missing opposite or hypotenuse without opening a full trigonometry worksheet.
Game, CAD, and right-triangle tooling
Recover a missing opposite or hypotenuse in a right-triangle mesh fragment or camera frustum when only the sine pairing is known in the scene graph.
FAQ
What does this sin triangle calculator compute?
It uses sin(θ) = opposite / hypotenuse in a right triangle. Given one acute angle and one of those two sides, it returns the missing side as value, plus the complementary acute angle.
Why must the angle be between 0 and 90 degrees?
In a right triangle the two remaining corners are acute.
How is the complementary angle related to sine?
The complementary acute angle is 90° minus the given angle from the right-triangle angle sum. The missing side itself is recovered from the sine ratio, not from that complement.
What does the sin triangle calculator cost?
The browser tool is free and runs locally.
Can I enter the adjacent side instead?
No. Sine links only the opposite side and the hypotenuse; the adjacent side belongs to cosine. If what you know is the adjacent side, a cosine or a general right-triangle solver is the right tool.
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/sin-triangle \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"angle":30,"side":5,"known_side":"opposite"}'const res = await fetch("https://api.kit.forhosting.com/math/sin-triangle", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"angle": 30,
"side": 5,
"known_side": "opposite"
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/sin-triangle",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"angle": 30,
"side": 5,
"known_side": "opposite"
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/sin-triangle", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"angle":30,"side":5,"known_side":"opposite"}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"angle":30,"side":5,"known_side":"opposite"}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/sin-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
{
"angle": 30,
"side": 5,
"known_side": "opposite"
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.sin_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
Angles must sit strictly between zero and ninety degrees; zero, ninety, and anything outside that open interval are rejected as invalid_input because they are not acute corners of a non-degenerate right triangle.
How to call the API and what the missing value looks like
Use it from geometry homework pipelines, roof-pitch and ramp scripts, game-level tooling, interview-prep sandboxes, or any workflow that needs a reproducible sine-only right-triangle solve without installing a computer-algebra package on every machine. Send a JSON body with three required fields. Field angle is the known acute angle in degrees, strictly greater than zero and strictly less than ninety; aliases theta and angle_deg are accepted. Field side is the known positive side length; aliases length and known_length map to the same meaning. Field known_side is the role of that length relative to the given angle and must be opposite or hypotenuse; aliases side_type and role are accepted, as are the short tokens opp, hyp, o, and h. On success the response echoes angle and known_side, adds complementary_angle as ninety minus the given angle, right_angle as ninety, both opposite and hypotenuse after the sine solve, missing as the name of the side that was not supplied, value as that missing length (the primary result), sine of the given angle, formula sin(θ) = opposite / hypotenuse, method sine, and unit_angle set to degrees. Failed validation — a missing required field, a non-finite number, a non-positive side, an angle at or outside the open zero-to-ninety interval, a known_side other than opposite or hypotenuse including adjacent, or a numerically degenerate configuration — returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item. Keep sides inside the published positive range up to one trillion so intermediate quotients stay finite in IEEE double precision on the Worker and in the browser.
Practical tips, limits, and when a sine-only solve is the right tool
Because sine of thirty, forty-five, and sixty degrees is taken from textbook exact values, students can recompute opposite and hypotenuse by hand for those specials and match the API line by line. This landing targets people searching for a sin triangle calculator or a sine right-triangle missing-side tool; it is not a full SOHCAHTOA solver, not a Pythagorean two-sides calculator, and not a law-of-sines tool for an oblique triangle. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when users type ninety degrees while learning that the right angle is already spoken for. Round-trip checks are easy: after solving, confirm that opposite divided by hypotenuse equals the returned sine within floating tolerance and that complementary_angle plus angle equals ninety.
Integration use cases
Homework and exam checks for SOH problems
Give students one acute angle and either the opposite or the hypotenuse; compare their hand-computed missing side and complementary angle against a deterministic API or free browser result.
Technical questions
Can I enter the adjacent side?
No. Sine pairs opposite with hypotenuse only. Adjacent belongs to cosine (or to sine of the complementary angle). known_side must be opposite or hypotenuse.