Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 120   b = 89.07   c = 136.46

Area: T = 5263.0065585
Perimeter: p = 345.53
Semiperimeter: s = 172.765

Angle ∠ A = α = 59.9999171812° = 59°59'57″ = 1.04771830966 rad
Angle ∠ B = β = 40.0011075681° = 40°4″ = 0.6988150475 rad
Angle ∠ C = γ = 809.9997525071° = 79°59'59″ = 1.3966259082 rad

Height: ha = 87.71767597499
Height: hb = 118.177684035
Height: hc = 77.13662389711

Median: ma = 98.3743768099
Median: mb = 120.5299247799
Median: mc = 80.69332435214

Inradius: r = 30.4633378491
Circumradius: R = 69.28326104991

Vertex coordinates: A[136.46; 0] B[0; 0] C[91.92438850213; 77.13662389711]
Centroid: CG[76.12879616738; 25.7122079657]
Coordinates of the circumscribed circle: U[68.23; 12.03110937813]
Coordinates of the inscribed circle: I[83.695; 30.4633378491]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120.0010828188° = 120°3″ = 1.04771830966 rad
∠ B' = β' = 139.9998924319° = 139°59'56″ = 0.6988150475 rad
∠ C' = γ' = 1000.000247493° = 100°1″ = 1.3966259082 rad

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How did we calculate this triangle?

a = 120 ; ; b = 89.07 ; ; c = 136.46 ; ;

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

p = a+b+c = 120+89.07+136.46 = 345.53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 345.53 }{ 2 } = 172.77 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 172.77 * (172.77-120)(172.77-89.07)(172.77-136.46) } ; ; T = sqrt{ 27699227.79 } = 5263.01 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5263.01 }{ 120 } = 87.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5263.01 }{ 89.07 } = 118.18 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5263.01 }{ 136.46 } = 77.14 ; ;

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{ 89.07**2+136.46**2-120**2 }{ 2 * 89.07 * 136.46 } ) = 59° 59'57" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 120**2+136.46**2-89.07**2 }{ 2 * 120 * 136.46 } ) = 40° 4" ; ; gamma = 180° - alpha - beta = 180° - 59° 59'57" - 40° 4" = 79° 59'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5263.01 }{ 172.77 } = 30.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 120 }{ 2 * sin 59° 59'57" } = 69.28 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 89.07**2+2 * 136.46**2 - 120**2 } }{ 2 } = 98.374 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 136.46**2+2 * 120**2 - 89.07**2 } }{ 2 } = 120.529 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 89.07**2+2 * 120**2 - 136.46**2 } }{ 2 } = 80.693 ; ;
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