Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 9.7   b = 11.8   c = 12.2

Area: T = 53.18994058413
Perimeter: p = 33.7
Semiperimeter: s = 16.85

Angle ∠ A = α = 47.64217941394° = 47°38'30″ = 0.83215061693 rad
Angle ∠ B = β = 64.01771511345° = 64°1'2″ = 1.1177310065 rad
Angle ∠ C = γ = 68.34110547261° = 68°20'28″ = 1.19327764193 rad

Height: ha = 10.96768878023
Height: hb = 9.01551535324
Height: hc = 8.72195747281

Median: ma = 10.97880462743
Median: mb = 9.30988667409
Median: mc = 8.91437534182

Inradius: r = 3.15766412962
Circumradius: R = 6.56333934893

Vertex coordinates: A[12.2; 0] B[0; 0] C[4.25495901639; 8.72195747281]
Centroid: CG[5.48331967213; 2.90765249094]
Coordinates of the circumscribed circle: U[6.1; 2.42224231868]
Coordinates of the inscribed circle: I[5.05; 3.15766412962]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.3588205861° = 132°21'30″ = 0.83215061693 rad
∠ B' = β' = 115.9832848865° = 115°58'58″ = 1.1177310065 rad
∠ C' = γ' = 111.6598945274° = 111°39'32″ = 1.19327764193 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 = 9.7+11.8+12.2 = 33.7 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 33.7 }{ 2 } = 16.85 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.85 * (16.85-9.7)(16.85-11.8)(16.85-12.2) } ; ; T = sqrt{ 2829.11 } = 53.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 53.19 }{ 9.7 } = 10.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 53.19 }{ 11.8 } = 9.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 53.19 }{ 12.2 } = 8.72 ; ;

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{ 11.8**2+12.2**2-9.7**2 }{ 2 * 11.8 * 12.2 } ) = 47° 38'30" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 9.7**2+12.2**2-11.8**2 }{ 2 * 9.7 * 12.2 } ) = 64° 1'2" ; ; gamma = 180° - alpha - beta = 180° - 47° 38'30" - 64° 1'2" = 68° 20'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 53.19 }{ 16.85 } = 3.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 9.7 }{ 2 * sin 47° 38'30" } = 6.56 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.8**2+2 * 12.2**2 - 9.7**2 } }{ 2 } = 10.978 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.2**2+2 * 9.7**2 - 11.8**2 } }{ 2 } = 9.309 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.8**2+2 * 9.7**2 - 12.2**2 } }{ 2 } = 8.914 ; ;
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