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Triangle Calculator: Solve SSS, SAS, ASA and AAS

Pick what you know, enter it, and the calculator finds the missing sides and angles, the area by Heron's formula, the perimeter and the type of triangle.

Area

14.6969cm²

Scalene, acute
Sides a · b · c
5 · 6 · 7 cm
Angles A · B · C
44.42° · 57.12° · 78.46°
Perimeter
18 cm
Height on side c
4.1991 cm
Show working
  1. cos A = (b² + c² − a²) / 2bc → A = 44.4153°
  2. cos B = (c² + a² − b²) / 2ca → B = 57.1217°
  3. C = 180° − A − B = 78.463°
  4. s = (a + b + c) / 2 = 9
  5. Area = √(s(s−a)(s−b)(s−c)) = 14.6969 cm²

How to use

  1. Choose SSS, SAS, ASA or AAS.
  2. Enter the sides and angles shown (side a is opposite angle A, and so on).
  3. Read the area, all sides and angles, and the triangle type.

Good to know

SSS uses the cosine rule to find the angles. SAS uses the cosine rule for the third side. ASA and AAS use the angle sum (180°) and the sine rule a/sin A = b/sin B = c/sin C. These are the same congruence cases you meet in NCERT Class 7 and 9.

Area is found with Heron's formula, A = √(s(s − a)(s − b)(s − c)) with s = (a + b + c)/2, the Class 9 method that needs no height. The height on side c is also shown.

The type is shown by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse). SSA (two sides and a non-included angle) is not offered because it can have two different answers.

Questions

What do SSS, SAS, ASA and AAS mean?

Side-side-side, side-angle-side (angle between the two sides), angle-side-angle (side between the two angles) and angle-angle-side.

What is Heron's formula?

Area = √(s(s − a)(s − b)(s − c)), where s is half the perimeter. For sides 3, 4, 5: s = 6, area = √(6 × 3 × 2 × 1) = 6.

Why does it say the sides cannot make a triangle?

Any two sides must add up to more than the third. 2, 3 and 6 fail because 2 + 3 is less than 6.

How do I know if a triangle is right-angled?

If the largest angle is 90°, or a² + b² = c² for the longest side c. The badge shows it.

Is anything I enter stored?

No. The calculation runs in your browser and nothing is sent to a server.

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