Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 7.6   b = 6.7   c = 3.57

Area: T = 11.95994591067
Perimeter: p = 17.87
Semiperimeter: s = 8.935

Angle ∠ A = α = 90.15498329819° = 90°8'59″ = 1.57334114057 rad
Angle ∠ B = β = 61.83330555179° = 61°49'59″ = 1.07991904054 rad
Angle ∠ C = γ = 28.01771115002° = 28°1'2″ = 0.48989908426 rad

Height: ha = 3.14772260807
Height: hb = 3.5769987793
Height: hc = 6.76999770906

Median: ma = 3.79217608047
Median: mb = 4.90220352916
Median: mc = 6.93882112248

Inradius: r = 1.3388495703
Circumradius: R = 3.88000129934

Vertex coordinates: A[3.57; 0] B[0; 0] C[3.58875210084; 6.76999770906]
Centroid: CG[2.38658403361; 2.23333256969]
Coordinates of the circumscribed circle: U[1.785; 3.35546793812]
Coordinates of the inscribed circle: I[2.235; 1.3388495703]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 89.85501670181° = 89°51'1″ = 1.57334114057 rad
∠ B' = β' = 118.1676944482° = 118°10'1″ = 1.07991904054 rad
∠ C' = γ' = 151.98328885° = 151°58'58″ = 0.48989908426 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 = 7.6+6.7+3.57 = 17.87 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 17.87 }{ 2 } = 8.94 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.94 * (8.94-7.6)(8.94-6.7)(8.94-3.57) } ; ; T = sqrt{ 143.03 } = 11.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11.96 }{ 7.6 } = 3.15 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11.96 }{ 6.7 } = 3.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11.96 }{ 3.57 } = 6.7 ; ;

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{ 6.7**2+3.57**2-7.6**2 }{ 2 * 6.7 * 3.57 } ) = 90° 8'59" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7.6**2+3.57**2-6.7**2 }{ 2 * 7.6 * 3.57 } ) = 61° 49'59" ; ; gamma = 180° - alpha - beta = 180° - 90° 8'59" - 61° 49'59" = 28° 1'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11.96 }{ 8.94 } = 1.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7.6 }{ 2 * sin 90° 8'59" } = 3.8 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.7**2+2 * 3.57**2 - 7.6**2 } }{ 2 } = 3.792 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.57**2+2 * 7.6**2 - 6.7**2 } }{ 2 } = 4.902 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.7**2+2 * 7.6**2 - 3.57**2 } }{ 2 } = 6.938 ; ;
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