Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 8.92   b = 7.83   c = 9.07

Area: T = 31.69991076922
Perimeter: p = 25.82
Semiperimeter: s = 12.91

Angle ∠ A = α = 63.21551534359° = 63°12'55″ = 1.10333125646 rad
Angle ∠ B = β = 51.59331214543° = 51°35'35″ = 0.99004698408 rad
Angle ∠ C = γ = 65.19217251098° = 65°11'30″ = 1.13878102482 rad

Height: ha = 7.10774232494
Height: hb = 8.09768346596
Height: hc = 6.99898804172

Median: ma = 7.20438392542
Median: mb = 8.09986681004
Median: mc = 7.06219703341

Inradius: r = 2.45553917655
Circumradius: R = 4.99660511361

Vertex coordinates: A[9.07; 0] B[0; 0] C[5.5411477398; 6.99898804172]
Centroid: CG[4.8770492466; 2.33299601391]
Coordinates of the circumscribed circle: U[4.535; 2.09662590381]
Coordinates of the inscribed circle: I[5.08; 2.45553917655]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 116.7854846564° = 116°47'5″ = 1.10333125646 rad
∠ B' = β' = 128.4076878546° = 128°24'25″ = 0.99004698408 rad
∠ C' = γ' = 114.808827489° = 114°48'30″ = 1.13878102482 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 = 8.92+7.83+9.07 = 25.82 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 25.82 }{ 2 } = 12.91 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.91 * (12.91-8.92)(12.91-7.83)(12.91-9.07) } ; ; T = sqrt{ 1004.83 } = 31.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 31.7 }{ 8.92 } = 7.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 31.7 }{ 7.83 } = 8.1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 31.7 }{ 9.07 } = 6.99 ; ;

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{ 7.83**2+9.07**2-8.92**2 }{ 2 * 7.83 * 9.07 } ) = 63° 12'55" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8.92**2+9.07**2-7.83**2 }{ 2 * 8.92 * 9.07 } ) = 51° 35'35" ; ; gamma = 180° - alpha - beta = 180° - 63° 12'55" - 51° 35'35" = 65° 11'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 31.7 }{ 12.91 } = 2.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8.92 }{ 2 * sin 63° 12'55" } = 5 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.83**2+2 * 9.07**2 - 8.92**2 } }{ 2 } = 7.204 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.07**2+2 * 8.92**2 - 7.83**2 } }{ 2 } = 8.099 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.83**2+2 * 8.92**2 - 9.07**2 } }{ 2 } = 7.062 ; ;
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