Tarife

Dreiecksrechner

Löse jedes Dreieck — nicht nur rechtwinklige — aus SSS, SWS oder WSW: alle Seiten, alle Winkel, Umfang, Flächeninhalt und Art des Dreiecks.

Die Seite a liegt dem Winkel A gegenüber

Ergebnis

Gib Werte ein und tippe auf Berechnen, um das Ergebnis zu sehen.

Formel

c2=a2+b2−2abcos⁡Cc^2 = a^2 + b^2 - 2ab\cos C

The law of cosines links three sides and one angle.

asin⁡A=bsin⁡B=csin⁡C\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

The law of sines: each side over the sine of its opposite angle is the same.

Area=s(s−a)(s−b)(s−c),s=a+b+c2\text{Area} = \sqrt{s(s-a)(s-b)(s-c)},\quad s = \frac{a+b+c}{2}

Heron’s formula gives the area from the three sides.

So benutzt du diesen Rechner

  1. Choose what you know: three sides, two sides and the angle between them, or two angles and the side between them.
  2. Side a is opposite angle A, side b opposite angle B and side c opposite angle C.
  3. Press Calculate to get every side, every angle, the perimeter, the area and the triangle type.

Gelöstes Beispiel

A triangle with sides 3, 4 and 5

Check the triangle inequality: 3 + 4 > 5, so the triangle exists.

Law of cosines: cos A = (16 + 25 − 9)/40 = 4/5, so A ≈ 36.869898°; cos B = 3/5, so B ≈ 53.130102°; cos C = 0, so C = 90°.

Heron: s = 6 and the area is √(6 × 3 × 2 × 1) = 6.

Häufig gestellte Fragen

Why does it say no triangle exists?

Any two sides must add up to more than the third side, and the angles must add up to exactly 180°.

Why is SSA (two sides and an angle not between them) not offered?

SSA can give two different triangles or none at all — the “ambiguous case”. Sumzo AI can walk through it.

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