Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 17.26   b = 18.44   c = 9.49

Area: T = 81.0177233909
Perimeter: p = 45.19
Semiperimeter: s = 22.595

Angle ∠ A = α = 67.81096979496° = 67°48'35″ = 1.1843502494 rad
Angle ∠ B = β = 81.58661992362° = 81°35'10″ = 1.42439478009 rad
Angle ∠ C = γ = 30.60441028141° = 30°36'15″ = 0.53441423587 rad

Height: ha = 9.38878602444
Height: hb = 8.78771186452
Height: hc = 17.07442326468

Median: ma = 11.85662198866
Median: mb = 10.43991307109
Median: mc = 17.21878853231

Inradius: r = 3.5865626639
Circumradius: R = 9.32203134391

Vertex coordinates: A[9.49; 0] B[0; 0] C[2.52655057956; 17.07442326468]
Centroid: CG[4.00551685985; 5.69114108823]
Coordinates of the circumscribed circle: U[4.745; 8.02220457243]
Coordinates of the inscribed circle: I[4.155; 3.5865626639]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.199030205° = 112°11'25″ = 1.1843502494 rad
∠ B' = β' = 98.41438007638° = 98°24'50″ = 1.42439478009 rad
∠ C' = γ' = 149.3965897186° = 149°23'45″ = 0.53441423587 rad

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How did we calculate this triangle?

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 17.26+18.44+9.49 = 45.19 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45.19 }{ 2 } = 22.6 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.6 * (22.6-17.26)(22.6-18.44)(22.6-9.49) } ; ; T = sqrt{ 6563.79 } = 81.02 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 81.02 }{ 17.26 } = 9.39 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 81.02 }{ 18.44 } = 8.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 81.02 }{ 9.49 } = 17.07 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos alpha ; ; alpha = arccos( fraction{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 18.44**2+9.49**2-17.26**2 }{ 2 * 18.44 * 9.49 } ) = 67° 48'35" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 17.26**2+9.49**2-18.44**2 }{ 2 * 17.26 * 9.49 } ) = 81° 35'10" ; ; gamma = 180° - alpha - beta = 180° - 67° 48'35" - 81° 35'10" = 30° 36'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 81.02 }{ 22.6 } = 3.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 17.26 }{ 2 * sin 67° 48'35" } = 9.32 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 18.44**2+2 * 9.49**2 - 17.26**2 } }{ 2 } = 11.856 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.49**2+2 * 17.26**2 - 18.44**2 } }{ 2 } = 10.439 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 18.44**2+2 * 17.26**2 - 9.49**2 } }{ 2 } = 17.218 ; ;
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