Measuring a figure 01 Pick a tab — Triangle, Plane, Solid or Coordinate — and inside Plane or Solid the shape. 02 Fill the fields you know: any three of a, b, c, A, B, C for a triangle, the required dimensions for a solid, the points for a coordinate tool. 03 Read the detected case first. Above a triangle result the panel prints a line such as Detected case: SAS — two sides + included angle → law of cosines. 04 Read the cards: area, perimeter, radii, heights, medians, bisectors and a centre table; the triangle is drawn to scale with Incircle, Circumcircle and Medians toggles. Verified readouts Every row was produced by this panel; the same inputs reproduce it.
Tool
Input
Readout
Triangle (SAS)
a = 5, b = 7, C = 60°
c = 6.245 ; A = 43.8979° , B = 76.1021° ; area 15.1554 ; circumradius 3.60555
Triangle (SSA)
a = 8, b = 10, A = 40°
two solutions: area 39.9269 (acute) and 9.31348 (obtuse)
Coordinate line
P₁(0, 1), P₂(2, 5)
y = 2x + 1 ; slope 2 ; inclination 63.4349° ; distance 4.472136
Polygon area
(0, 0), (4, 0), (4, 3), (0, 3)
area 12 ; signed area 12 (CCW); centroid (2, 1.5)
The SAS case is the law of cosines in action: the missing side is 6.245 and the remaining angles follow from it.
Where the numbers stop
Three parts, not three angles. A = 50°, B = 60°, C = 70° returns AAA fixes only the shape — supply one side; sides must satisfy the triangle inequality and angles stay below 180°.
Coordinates are canonical. A triangle is reconstructed with A at the origin and B on the +x axis (the Centre (A at origin, B on +x) label), so the drawn coordinates are a standard placement, not the original survey position; use Coordinate for real points. What it does not do: the analytic tabs return fixed measurements, not a draggable construction, and do not inspect 3D models — the Dynamic Geometry and Model Inspector surfaces on the same page cover those. A coordinate rotation is a matrix operation, checked in the matrix panel . The SSA case is genuinely ambiguous With two sides and a non-included angle the sine rule can fit two different triangles, and the panel says so: Detected case: SSA — two sides + opposite angle → may be ambiguous · ambiguous: two solutions. For a = 8, b = 10, A = 40°, one solution is acute scalene (B = 53.4641° , C = 86.5359° , area 39.9269 ), the other obtuse scalene (B = 126.536° , C = 13.4641° , area 9.31348 ). Both satisfy the data and share the circumradius 6.2229 , so an extra condition (an altitude, a maximum angle, a diagram) must pick one.
Where it fits Framing and trusses A bay given as two members and the included angle (a = 5, b = 7, C = 60°) yields the third member 6.245 and area 15.1554 — enough to cut a brace without drawing it.
Circular layouts and plot areas Pins at (0, 0), (4, 0) and (0, 3) define (x − 2)² + (y − 1.5)² = 6.25 : centre (2, 1.5), radius 2.5 , area 19.63495 . Corners entered one per line — (0, 0), (4, 0), (4, 3), (0, 3) — give area 12 , orientation CCW ; the signed value flips for clockwise input. A cone with r = 3, h = 4 returns volume 37.69911 and surface 75.39822 .
Privacy All tabs compute inside your browser; the measurements you enter and the results are never uploaded.
References
Wikipedia, Solution of triangles , en.wikipedia.org （访问日期：2026-10-01）— the SSS, SAS, ASA, AAS and SSA cases.
Wikipedia, Law of sines , en.wikipedia.org （访问日期：2026-10-01）— the ambiguous SSA configuration.
Wikipedia, Shoelace formula , en.wikipedia.org （访问日期：2026-10-01）— signed polygon area and orientation.
Eric W. Weisstein, Triangle , MathWorld, mathworld.wolfram.com （访问日期：2026-10-01）— circumradius, inradius and derived lengths.
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Reviewed by CalcX Editorial Team
Updated 2026-10-01