Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 1.27   b = 3.78   c = 4.54

Area: T = 2.09215920275
Perimeter: p = 9.59
Semiperimeter: s = 4.795

Angle ∠ A = α = 14.10884619557° = 14°6'30″ = 0.24662391135 rad
Angle ∠ B = β = 46.51218462318° = 46°30'43″ = 0.81217848579 rad
Angle ∠ C = γ = 119.3879691812° = 119°22'47″ = 2.08435686821 rad

Height: ha = 3.29438457126
Height: hb = 1.10766624484
Height: hc = 0.92114061795

Median: ma = 4.12987740311
Median: mb = 2.74659333568
Median: mc = 1.67326476019

Inradius: r = 0.43662027169
Circumradius: R = 2.60550400501

Vertex coordinates: A[4.54; 0] B[0; 0] C[0.87440198238; 0.92114061795]
Centroid: CG[1.80546732746; 0.30771353932]
Coordinates of the circumscribed circle: U[2.27; -1.27880194296]
Coordinates of the inscribed circle: I[1.015; 0.43662027169]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.8921538044° = 165°53'30″ = 0.24662391135 rad
∠ B' = β' = 133.4888153768° = 133°29'17″ = 0.81217848579 rad
∠ C' = γ' = 60.62203081876° = 60°37'13″ = 2.08435686821 rad

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How did we calculate this triangle?

a = 1.27 ; ; b = 3.78 ; ; c = 4.54 ; ;

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

p = a+b+c = 1.27+3.78+4.54 = 9.59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 9.59 }{ 2 } = 4.8 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4.8 * (4.8-1.27)(4.8-3.78)(4.8-4.54) } ; ; T = sqrt{ 4.37 } = 2.09 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.09 }{ 1.27 } = 3.29 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.09 }{ 3.78 } = 1.11 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.09 }{ 4.54 } = 0.92 ; ;

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{ 3.78**2+4.54**2-1.27**2 }{ 2 * 3.78 * 4.54 } ) = 14° 6'30" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1.27**2+4.54**2-3.78**2 }{ 2 * 1.27 * 4.54 } ) = 46° 30'43" ; ; gamma = 180° - alpha - beta = 180° - 14° 6'30" - 46° 30'43" = 119° 22'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.09 }{ 4.8 } = 0.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1.27 }{ 2 * sin 14° 6'30" } = 2.61 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.78**2+2 * 4.54**2 - 1.27**2 } }{ 2 } = 4.129 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.54**2+2 * 1.27**2 - 3.78**2 } }{ 2 } = 2.746 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.78**2+2 * 1.27**2 - 4.54**2 } }{ 2 } = 1.673 ; ;
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