Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 1.13   b = 0.9   c = 0.68

Area: T = 0.3065997932
Perimeter: p = 2.71
Semiperimeter: s = 1.355

Angle ∠ A = α = 90.21106467227° = 90°12'38″ = 1.57444728057 rad
Angle ∠ B = β = 52.79328813676° = 52°47'34″ = 0.92114096015 rad
Angle ∠ C = γ = 36.99664719097° = 36°59'47″ = 0.64657102464 rad

Height: ha = 0.54215892601
Height: hb = 0.68799954044
Height: hc = 0.98999939176

Median: ma = 0.56330053286
Median: mb = 0.81767925073
Median: mc = 0.9633249708

Inradius: r = 0.22658287321
Circumradius: R = 0.56550038184

Vertex coordinates: A[0.68; 0] B[0; 0] C[0.68333088235; 0.98999939176]
Centroid: CG[0.45444362745; 0.32999979725]
Coordinates of the circumscribed circle: U[0.34; 0.45112530497]
Coordinates of the inscribed circle: I[0.455; 0.22658287321]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 89.78993532773° = 89°47'22″ = 1.57444728057 rad
∠ B' = β' = 127.2077118632° = 127°12'26″ = 0.92114096015 rad
∠ C' = γ' = 143.004352809° = 143°13″ = 0.64657102464 rad

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How did we calculate this triangle?

a = 1.13 ; ; b = 0.9 ; ; c = 0.68 ; ;

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

p = a+b+c = 1.13+0.9+0.68 = 2.71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2.71 }{ 2 } = 1.36 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1.36 * (1.36-1.13)(1.36-0.9)(1.36-0.68) } ; ; T = sqrt{ 0.09 } = 0.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.31 }{ 1.13 } = 0.54 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.31 }{ 0.9 } = 0.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.31 }{ 0.68 } = 0.9 ; ;

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{ 0.9**2+0.68**2-1.13**2 }{ 2 * 0.9 * 0.68 } ) = 90° 12'38" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1.13**2+0.68**2-0.9**2 }{ 2 * 1.13 * 0.68 } ) = 52° 47'34" ; ; gamma = 180° - alpha - beta = 180° - 90° 12'38" - 52° 47'34" = 36° 59'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.31 }{ 1.36 } = 0.23 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1.13 }{ 2 * sin 90° 12'38" } = 0.57 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.9**2+2 * 0.68**2 - 1.13**2 } }{ 2 } = 0.563 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.68**2+2 * 1.13**2 - 0.9**2 } }{ 2 } = 0.817 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.9**2+2 * 1.13**2 - 0.68**2 } }{ 2 } = 0.963 ; ;
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