Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 5.7   b = 4   c = 2

Area: T = 2.549999875
Perimeter: p = 11.7
Semiperimeter: s = 5.85

Angle ∠ A = α = 141.3187835483° = 141°19'4″ = 2.4666461521 rad
Angle ∠ B = β = 26.01443520182° = 26°52″ = 0.45440360955 rad
Angle ∠ C = γ = 12.66878124986° = 12°40'4″ = 0.22110950371 rad

Height: ha = 0.87771925439
Height: hb = 1.2549999375
Height: hc = 2.549999875

Median: ma = 1.37702189606
Median: mb = 3.77442548934
Median: mc = 4.82113068768

Inradius: r = 0.42773502137
Circumradius: R = 4.566000228

Vertex coordinates: A[2; 0] B[0; 0] C[5.12325; 2.549999875]
Centroid: CG[2.37441666667; 0.83333329167]
Coordinates of the circumscribed circle: U[1; 4.44990022245]
Coordinates of the inscribed circle: I[1.85; 0.42773502137]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 38.68221645168° = 38°40'56″ = 2.4666461521 rad
∠ B' = β' = 153.9865647982° = 153°59'8″ = 0.45440360955 rad
∠ C' = γ' = 167.3322187501° = 167°19'56″ = 0.22110950371 rad

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How did we calculate this triangle?

a = 5.7 ; ; b = 4 ; ; c = 2 ; ;

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

p = a+b+c = 5.7+4+2 = 11.7 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.7 }{ 2 } = 5.85 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.85 * (5.85-5.7)(5.85-4)(5.85-2) } ; ; T = sqrt{ 6.25 } = 2.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.5 }{ 5.7 } = 0.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.5 }{ 4 } = 1.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.5 }{ 2 } = 2.5 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 5.7**2-4**2-2**2 }{ 2 * 4 * 2 } ) = 141° 19'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4**2-5.7**2-2**2 }{ 2 * 5.7 * 2 } ) = 26° 52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2**2-5.7**2-4**2 }{ 2 * 4 * 5.7 } ) = 12° 40'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.5 }{ 5.85 } = 0.43 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5.7 }{ 2 * sin 141° 19'4" } = 4.56 ; ;

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